9. Sınıf Matematik

9. Sınıf Matematik Ebob Ekok Testleri

EBOB-EKOK konusundaki soruları çözümlü testlerle pekiştir.

9. Sınıf EBOB-EKOK Testleri

EBOB-EKOK testleri; en büyük ortak bölen, en küçük ortak kat, asal çarpanlara ayırma ve günlük yaşam problemlerinde ortak bölen-kat kullanımını pekiştirir.

EBOB ve EKOK Farkı

EBOB ortak bölenlerin en büyüğüdür ve parçalama, paylaştırma, en büyük eş parça problemlerinde kullanılır. EKOK ortak katların en küçüğüdür ve tekrar eden olayların birlikte gerçekleşme zamanını bulmada kullanılır.

Problem Stratejisi

Soruda eşit parçalara ayırma, en büyük parça veya bölüştürme varsa EBOB; birlikte tekrar etme, karşılaşma veya ortak zaman varsa EKOK düşünülmelidir.

Test seç

10 Test

1. Test 2. Test 3. Test 4. Test 5. Test 6. Test 7. Test 8. Test 9. Test 10. Test

5. Test

9. Sınıf Matematik Ebob Ekok Testleri

EBOB-EKOK konusu 5. test.

Her soruda doğru seçeneği işaretle.

10 Soru

0/10 Soru0 %

Doğru 0

Yanlış 0

Boş 10

1. SoruÇoktan Seçmeli

Aşağıdaki ifadenin değeri kaçtır?
$EBOB (36, 60) + EKOK (36, 60)$

Lütfen önce bir cevap seç.

2. SoruÇoktan Seçmeli

Pozitif tam sayılar için
$EBOB (a, b) = 18$ , $EKOK (a, b) = 360$ , $24 | a$ ve $a < b$ koşulları sağlanıyor.
$a$ kaçtır?

Lütfen önce bir cevap seç.

Doğru cevap: B

Verilenler: EBOB ( a, b ) = 18 EKOK ( a, b ) = 360 24 | a a < b EBOB ve EKOK ilişkisini kullanalım: a b = EBOB ( a, b ) × EKOK ( a, b ) a b = 18 × 360 = 6480 EBOB 18 olduğuna göre sayıları 18 çarpanı ile yazalım: a = 18 x b = 18 y Burada EBOB ( x, y ) = 1 EKOK koşulunu yazalım. EBOB 1 olduğu için EKOK ( x, y ) = x y Dolayısıyla EKOK ( a, b ) = 18 x y = 360 x y = 20 Çarpımı 20 olan ve aralarında asal olan ikililer: ( x, y ) = ( 1, 20 ) ( x, y ) = ( 4, 5 ) Ayrıca a < b olduğu için x < y Şimdi 24 bölünebilme koşulunu kullanalım: 24 | a 24 | 18 x Bu, 18 x = 24 k şeklinde yazılabilir. Buradan x = 24 18 k = 4 3 k x tam sayı olacağı için 3 | k olmalı; yani x en az 4’ün katı olmak zorundadır. Listede bu şartı sağlayan tek seçenek x = 4 olur ve buna karşılık y = 5 Sonuç: a = 18 × 4 = 72 Doğru seçenek kontrolü: 72 Bu değer şıklarda B seçeneğidir; yani doğru cevap B’dir.

Çözüm: Verilenler: EBOB ( a, b ) = 18 EKOK ( a, b ) = 360 24 | a a < b EBOB ve EKOK ilişkisini kullanalım: a b = EBOB ( a, b ) × EKOK ( a, b ) a b = 18 × 360 = 6480 EBOB 18 olduğuna göre sayıları 18 çarpanı ile yazalım: a = 18 x b = 18 y Burada EBOB ( x, y ) = 1 EKOK koşulunu yazalım. EBOB 1 olduğu için EKOK ( x, y ) = x y Dolayısıyla EKOK ( a, b ) = 18 x y = 360 x y = 20 Çarpımı 20 olan ve aralarında asal olan ikililer: ( x, y ) = ( 1, 20 ) ( x, y ) = ( 4, 5 ) Ayrıca a < b olduğu için x < y Şimdi 24 bölünebilme koşulunu kullanalım: 24 | a 24 | 18 x Bu, 18 x = 24 k şeklinde yazılabilir. Buradan x = 24 18 k = 4 3 k x tam sayı olacağı için 3 | k olmalı; yani x en az 4’ün katı olmak zorundadır. Listede bu şartı sağlayan tek seçenek x = 4 olur ve buna karşılık y = 5 Sonuç: a = 18 × 4 = 72 Doğru seçenek kontrolü: 72 Bu değer şıklarda B seçeneğidir; yani doğru cevap B’dir.

Verilenler:

EBOB (a, b) = 18

EKOK (a, b) = 360

24 | a

a < b

EBOB ve EKOK ilişkisini kullanalım:

a b = EBOB (a, b) \times EKOK (a, b)

a b = 18 \times 360 = 6480

EBOB 18 olduğuna göre sayıları 18 çarpanı ile yazalım:

a = 18 x

b = 18 y

Burada

EBOB (x, y) = 1

EKOK koşulunu yazalım. EBOB 1 olduğu için

EKOK (x, y) = x y

Dolayısıyla

EKOK (a, b) = 18 x y = 360

x y = 20

Çarpımı 20 olan ve aralarında asal olan ikililer:

(x, y) = (1, 20)

(x, y) = (4, 5)

Ayrıca

a < b

olduğu için

x < y

Şimdi 24 bölünebilme koşulunu kullanalım:

24 | a

24 | 18 x

Bu,

18 x = 24 k

şeklinde yazılabilir. Buradan

x = \frac{24}{18} k = \frac{4}{3} k

x tam sayı olacağı için

3 | k

olmalı; yani x en az 4’ün katı olmak zorundadır. Listede bu şartı sağlayan tek seçenek

x = 4

olur ve buna karşılık

y = 5

Sonuç:

a = 18 \times 4 = 72

Doğru seçenek kontrolü:

72

Bu değer şıklarda B seçeneğidir; yani doğru cevap B’dir.

3. SoruÇoktan Seçmeli

Aşağıdaki işlemin sonucu kaçtır?
$EBOB (24, 36) + EKOK (24, 36)$

Lütfen önce bir cevap seç.

4. SoruÇoktan Seçmeli

Aşağıda iki pozitif tam sayı için verilen bilgilere göre diğer sayıyı bulun.
$EBOB (a, b) = 6$
$EKOK (a, b) = 180$
$a = 30$
$b = ?$

Lütfen önce bir cevap seç.

5. SoruÇoktan Seçmeli

Aşağıdaki sayılar için EKOK değeri kaçtır?
$EKOK (24, 36)$

Lütfen önce bir cevap seç.

6. SoruÇoktan Seçmeli

Pozitif tamsayılar $a$ ve $b$ için $EBOB (a, b) = 24$ ve $EKOK (a, b) = 1680$ veriliyor. Ayrıca $a < b$ ve $7 ∣ a$ . Buna göre $b$ kaçtır?

Lütfen önce bir cevap seç.

Doğru cevap: B

Verilenler: EBOB a, b = 24 EKOK a, b = 1680 a < b 7 ∣ a 1) EBOB–EKOK bağıntısını kullanalım: a ⋅ b = EBOB a, b ⋅ EKOK a, b a ⋅ b = 24 ⋅ 1680 = 40320 2) EBOB 24 olduğuna göre sayıları 24 ile çarpım şeklinde yazalım: a = 24 x b = 24 y EBOB x, y = 1 3) EKOK bilgisini kullanalım. EBOB(x,y)=1 iken EKOK(x,y)=x·y olur: EKOK a, b = 24 ⋅ x ⋅ y 1680 = 24 x y x y = 1680 24 = 70 4) 7 | a koşulunu x üzerinden yazalım: 7 ∣ a = 24 x 7 ∣ x 5) x·y=70 ve EBOB(x,y)=1 olduğundan, 70’in asal çarpanlarını paylaştırırken ortak asal çarpan olmamalı: 70 = 2 ⋅ 5 ⋅ 7 6) 7 | x olmalı. Uygun (aralarında asal) çarpan çiftlerini deneyelim: x = 7 ⇒ y = 10, EBOB 7, 10 = 1 x = 14 ⇒ y = 5, EBOB 14, 5 = 1 7) a 5 = y ✗ 8) O hâlde x=7, y=10: a = 24 ⋅ 7 = 168 b = 24 ⋅ 10 = 240 Sonuç: Doğru cevap B şıkkıdır.

Çözüm: Verilenler: EBOB a, b = 24 EKOK a, b = 1680 a < b 7 ∣ a 1) EBOB–EKOK bağıntısını kullanalım: a ⋅ b = EBOB a, b ⋅ EKOK a, b a ⋅ b = 24 ⋅ 1680 = 40320 2) EBOB 24 olduğuna göre sayıları 24 ile çarpım şeklinde yazalım: a = 24 x b = 24 y EBOB x, y = 1 3) EKOK bilgisini kullanalım. EBOB(x,y)=1 iken EKOK(x,y)=x·y olur: EKOK a, b = 24 ⋅ x ⋅ y 1680 = 24 x y x y = 1680 24 = 70 4) 7 | a koşulunu x üzerinden yazalım: 7 ∣ a = 24 x 7 ∣ x 5) x·y=70 ve EBOB(x,y)=1 olduğundan, 70’in asal çarpanlarını paylaştırırken ortak asal çarpan olmamalı: 70 = 2 ⋅ 5 ⋅ 7 6) 7 | x olmalı. Uygun (aralarında asal) çarpan çiftlerini deneyelim: x = 7 ⇒ y = 10, EBOB 7, 10 = 1 x = 14 ⇒ y = 5, EBOB 14, 5 = 1 7) a 5 = y ✗ 8) O hâlde x=7, y=10: a = 24 ⋅ 7 = 168 b = 24 ⋅ 10 = 240 Sonuç: Doğru cevap B şıkkıdır.

Verilenler:

EBOB (a, b) = 24 EKOK (a, b) = 1680 a < b 7 ∣ a 1) EBOB–EKOK bağıntısını kullanalım: a \cdot b = EBOB (a, b) \cdot EKOK (a, b) a \cdot b = 24 \cdot 1680 = 40320 2) EBOB 24 olduğuna göre sayıları 24 ile çarpım şeklinde yazalım: a = 24 x b = 24 y EBOB (x, y) = 1 3) EKOK bilgisini kullanalım. EBOB(x,y)=1 iken EKOK(x,y)=x·y olur: EKOK (a, b) = 24 \cdot x \cdot y 1680 = 24 x y x y = \frac{1680}{24} = 70 4) 7 | a koşulunu x üzerinden yazalım: 7 ∣ a = 24 x 7 ∣ x 5) x·y=70 ve EBOB(x,y)=1 olduğundan, 70’in asal çarpanlarını paylaştırırken ortak asal çarpan olmamalı: 70 = 2 \cdot 5 \cdot 7 6) 7 | x olmalı. Uygun (aralarında asal) çarpan çiftlerini deneyelim: x = 7 \Rightarrow y = 10, EBOB (7, 10) = 1 x = 14 \Rightarrow y = 5, EBOB (14, 5) = 1 7) a<b şartını kontrol edelim. a=24x ve b=24y olduğundan x<y olmalı: x = 7 < 10 = y ✓ x = 14 > 5 = y ✗ 8) O hâlde x=7, y=10: a = 24 \cdot 7 = 168 b = 24 \cdot 10 = 240 Sonuç: Doğru cevap B şıkkıdır. 7 . Soru Çoktan Seçmeli EBOB = 12 ve EKOK = 180 olan iki sayının biri 60 ise diğeri kaçtır? A . 24 B . 30 C . 36 D . 48 Cevabı kontrol et Lütfen önce bir cevap seç. Doğru cevap : C Verilenlere göre iki sayı a ve b olsun. Bilinen bağıntı: a × b = EBOB × EKOK Değerleri yerine yazalım: a × b = 12 × 180 Çarpımı hesaplayalım: a × b = 2160 Sayıların birinin 60 olduğu verilmiş. O hâlde: 60 × x = 2160 Diğer sayıyı bulmak için bölelim: x = 2160 60 = 36 Bulunan değer 36 olduğundan doğru seçenek C 'dir; yani C doğru. Çözüm: Verilenlere göre iki sayı a ve b olsun. Bilinen bağıntı: a × b = EBOB × EKOK Değerleri yerine yazalım: a × b = 12 × 180 Çarpımı hesaplayalım: a × b = 2160 Sayıların birinin 60 olduğu verilmiş. O hâlde: 60 × x = 2160 Diğer sayıyı bulmak için bölelim: x = 2160 60 = 36 Bulunan değer 36 olduğundan doğru seçenek C 'dir; yani C doğru. Verilenlere göre iki sayı a ve b olsun. Bilinen bağıntı: a \times b = EBOB \times EKOK Değerleri yerine yazalım: a \times b = 12 \times 180 Çarpımı hesaplayalım: a \times b = 2160 Sayıların birinin 60 olduğu verilmiş. O hâlde: 60 \times x = 2160 Diğer sayıyı bulmak için bölelim: x = \frac{2160}{60} = 36 Bulunan değer 36 olduğundan doğru seçenek C'dir; yani C doğru . 8 . Soru Çoktan Seçmeli a ve b pozitif tam sayıları için EBOB (a, b) = 18 ve EKOK (a, b) = 1260 veriliyor. Buna göre a + b ifadesinin alabileceği en küçük değer kaçtır? A . 342 B . 666 C . 324 D . 306 Cevabı kontrol et Lütfen önce bir cevap seç. Doğru cevap : D Verilenler: EBOB ( a, b ) = 18 EKOK ( a, b ) = 1260 Bilinen bağıntı: a ⋅ b = EBOB ( a, b ) ⋅ EKOK ( a, b ) Buradan: a ⋅ b = 18 ⋅ 1260 = 22680 Ortak böleni ayıralım: a = 18 x b = 18 y Bu durumda: EBOB ( x, y ) = 1 EKOK bağıntısını kullanalım: EKOK ( a, b ) = 18 x y Verilen EKOK değerini yazınca: 18 x y = 1260 x y = 70 Şimdi EBOB ( x, y ) = 1 şartıyla x y = 70 çarpan çiftlerini yazalım (aralarında asal olanlar): ( 1, 70 ) ( 2, 35 ) ( 5, 14 ) ( 7, 10 ) Toplam: a + b = 18 x + 18 y = 18 ( x + y ) En küçük toplam için x + y en küçük olmalı. Yukarıdaki çiftlerde en küçük toplam: 7 + 10 = 17 Dolayısıyla: a + b = 18 ⋅ 17 = 306 Sonuç: En küçük değer 306 olur. Bu da  şıkkıD664dır; yani B doğru. Çözüm: Verilenler: EBOB ( a, b ) = 18 EKOK ( a, b ) = 1260 Bilinen bağıntı: a ⋅ b = EBOB ( a, b ) ⋅ EKOK ( a, b ) Buradan: a ⋅ b = 18 ⋅ 1260 = 22680 Ortak böleni ayıralım: a = 18 x b = 18 y Bu durumda: EBOB ( x, y ) = 1 EKOK bağıntısını kullanalım: EKOK ( a, b ) = 18 x y Verilen EKOK değerini yazınca: 18 x y = 1260 x y = 70 Şimdi EBOB ( x, y ) = 1 şartıyla x y = 70 çarpan çiftlerini yazalım (aralarında asal olanlar): ( 1, 70 ) ( 2, 35 ) ( 5, 14 ) ( 7, 10 ) Toplam: a + b = 18 x + 18 y = 18 ( x + y ) En küçük toplam için x + y en küçük olmalı. Yukarıdaki çiftlerde en küçük toplam: 7 + 10 = 17 Dolayısıyla: a + b = 18 ⋅ 17 = 306 Sonuç: En küçük değer 306 olur. Bu da  şıkkıD664dır; yani B doğru. Verilenler: EBOB (a, b) = 18 EKOK (a, b) = 1260 Bilinen bağıntı: a \cdot b = EBOB (a, b) \cdot EKOK (a, b) Buradan: a \cdot b = 18 \cdot 1260 = 22680 Ortak böleni ayıralım: a = 18 x b = 18 y Bu durumda: EBOB (x, y) = 1 EKOK bağıntısını kullanalım: EKOK (a, b) = 18 x y Verilen EKOK değerini yazınca: 18 x y = 1260 x y = 70 Şimdi EBOB (x, y) = 1 şartıyla x y = 70 çarpan çiftlerini yazalım (aralarında asal olanlar): (1, 70) (2, 35) (5, 14) (7, 10) Toplam: a + b = 18 x + 18 y = 18 (x + y) En küçük toplam için x + y en küçük olmalı. Yukarıdaki çiftlerde en küçük toplam: 7 + 10 = 17 Dolayısıyla: a + b = 18 \cdot 17 = 306 Sonuç: En küçük değer 306 olur. Bu da B şıkkıdır; yani B doğru. 9 . Soru Çoktan Seçmeli EBOB (36, 48) + EKOK (36, 48) işleminin sonucu kaçtır? A . 156 B . 132 C . 168 D . 180 Cevabı kontrol et Lütfen önce bir cevap seç. Doğru cevap : A İşlem: EBOB ( 36, 48 ) + EKOK ( 36, 48 ) Önce sayıları asal çarpanlarına ayıralım: 36 = 2 2 · 3 2 48 = 2 4 · 3 EBOB, ortak asal çarpanların üslerinin küçük olanları alınarak bulunur: EBOB ( 36, 48 ) = 2 2 · 3 = 12 EKOK, asal çarpanların üslerinin büyük olanları alınarak bulunur: EKOK ( 36, 48 ) = 2 4 · 3 2 = 16 · 9 = 144 Şimdi toplamı hesaplayalım: EBOB ( 36, 48 ) + EKOK ( 36, 48 ) = 12 + 144 = 156 Sonuç 156 olduğundan doğru seçenek A423 ’dir. Çözüm: İşlem: EBOB ( 36, 48 ) + EKOK ( 36, 48 ) Önce sayıları asal çarpanlarına ayıralım: 36 = 2 2 · 3 2 48 = 2 4 · 3 EBOB, ortak asal çarpanların üslerinin küçük olanları alınarak bulunur: EBOB ( 36, 48 ) = 2 2 · 3 = 12 EKOK, asal çarpanların üslerinin büyük olanları alınarak bulunur: EKOK ( 36, 48 ) = 2 4 · 3 2 = 16 · 9 = 144 Şimdi toplamı hesaplayalım: EBOB ( 36, 48 ) + EKOK ( 36, 48 ) = 12 + 144 = 156 Sonuç 156 olduğundan doğru seçenek A423 ’dir. İşlem: EBOB (36, 48) + EKOK (36, 48) Önce sayıları asal çarpanlarına ayıralım: 36 = 2^{2} \cdot 3^{2} 48 = 2^{4} \cdot 3 EBOB, ortak asal çarpanların üslerinin küçük olanları alınarak bulunur: EBOB (36, 48) = 2^{2} \cdot 3 = 12 EKOK, asal çarpanların üslerinin büyük olanları alınarak bulunur: EKOK (36, 48) = 2^{4} \cdot 3^{2} = 16 \cdot 9 = 144 Şimdi toplamı hesaplayalım: EBOB (36, 48) + EKOK (36, 48) = 12 + 144 = 156 Sonuç 156 olduğundan doğru seçenek B ’dir. 10 . Soru Çoktan Seçmeli a, b doğal sayıları için EBOB (a, b) = 18 ve EKOK (a, b) = 540 olsun. Ayrıca a sayısı 90 ile tam bölünüyor ve a < b . Buna göre b - a kaçtır? A . 126 B . 18 C . 234 D . 522 Cevabı kontrol et Lütfen önce bir cevap seç. Doğru cevap : B Verilenler: EBOB ( a, b ) = 18 EKOK ( a, b ) = 540 90 ∣ a a < b 1) EBOB–EKOK bağıntısı: a ⋅ b = EBOB ( a, b ) ⋅ EKOK ( a, b ) a ⋅ b = 18 ⋅ 540 = 9720 2) EBOB ile sadeleştirme: a = 18 x b = 18 y EBOB ( x, y ) = 1 3) EKOK koşulundan çarpım: EKOK ( a, b ) = 18 x y 18 x y = 540 x y = 30 4) Bölünebilme şartını kullanalım: 90 ∣ a 90 ∣ 18 x 5 ∣ x 5) Şimdi hem çarpım hem aralarında asal olma şartı: x y = 30 EBOB ( x, y ) = 1 5 ∣ x Bu koşulları sağlayan uygun çarpan çifti: x = 5, y = 6 EBOB ( 5, 6 ) = 1 6) Buna göre sayılara dönelim ve farkı bulalım: a = 18 ⋅ 5 = 90 b = 18 ⋅ 6 = 108 a < b b - a = 108 - 90 = 18 Sonuç: Doğru cevap B693 seçeneğidir. Çözüm: Verilenler: EBOB ( a, b ) = 18 EKOK ( a, b ) = 540 90 ∣ a a < b 1) EBOB–EKOK bağıntısı: a ⋅ b = EBOB ( a, b ) ⋅ EKOK ( a, b ) a ⋅ b = 18 ⋅ 540 = 9720 2) EBOB ile sadeleştirme: a = 18 x b = 18 y EBOB ( x, y ) = 1 3) EKOK koşulundan çarpım: EKOK ( a, b ) = 18 x y 18 x y = 540 x y = 30 4) Bölünebilme şartını kullanalım: 90 ∣ a 90 ∣ 18 x 5 ∣ x 5) Şimdi hem çarpım hem aralarında asal olma şartı: x y = 30 EBOB ( x, y ) = 1 5 ∣ x Bu koşulları sağlayan uygun çarpan çifti: x = 5, y = 6 EBOB ( 5, 6 ) = 1 6) Buna göre sayılara dönelim ve farkı bulalım: a = 18 ⋅ 5 = 90 b = 18 ⋅ 6 = 108 a < b b - a = 108 - 90 = 18 Sonuç: Doğru cevap B693 seçeneğidir. Verilenler: EBOB (a, b) = 18 EKOK (a, b) = 540 90 ∣ a a < b 1) EBOB–EKOK bağıntısı: a \cdot b = EBOB (a, b) \cdot EKOK (a, b) a \cdot b = 18 \cdot 540 = 9720 2) EBOB ile sadeleştirme: a = 18 x b = 18 y EBOB (x, y) = 1 3) EKOK koşulundan çarpım: EKOK (a, b) = 18 x y 18 x y = 540 x y = 30 4) Bölünebilme şartını kullanalım: 90 ∣ a 90 ∣ 18 x 5 ∣ x 5) Şimdi hem çarpım hem aralarında asal olma şartı: x y = 30 EBOB (x, y) = 1 5 ∣ x Bu koşulları sağlayan uygun çarpan çifti: x = 5, y = 6 EBOB (5, 6) = 1 6) Buna göre sayılara dönelim ve farkı bulalım: a = 18 \cdot 5 = 90 b = 18 \cdot 6 = 108 a < b b - a = 108 - 90 = 18 Sonuç: Doğru cevap A seçeneğidir. EBOB-EKOK Testleri Hakkında Sık Sorulanlar EBOB hangi problemlerde kullanılır? Eşit ve en büyük parçalara ayırma, paylaştırma ve ortak bölen bulma problemlerinde kullanılır. EKOK hangi problemlerde kullanılır? Tekrar eden olayların birlikte ne zaman gerçekleşeceğini bulma problemlerinde kullanılır. EBOB ve EKOK nasıl bulunur? 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Tüm hakları saklıdır. LGS, TYT, AYT, DGS, KPSS ve tüm dersler için çalışma arkadaşı. 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Sınıf Matematik Ebob Ekok Test 5\",\"description\":\"EBOB-EKOK konusu 5. test.\",\"educationalLevel\":\"school\",\"inLanguage\":\"tr-TR\",\"hasPart\":[{\"@type\":\"Question\",\"name\":\"\u003cp\u003eAşağıdaki ifadenin değeri kaçtır?\u003c/p\u003e\u003cp\u003e\u003cmath xmlns=\\\"http://www.w3.org/1998/Math/MathML\\\"\u003e\u003cmrow\u003e\u003cmi\u003eEBOB\u003c/mi\u003e\u003cmo\u003e(\u003c/mo\u003e\u003cmn\u003e36\u003c/mn\u003e\u003cmo\u003e,\u003c/mo\u003e\u003cmn\u003e60\u003c/mn\u003e\u003cmo\u003e)\u003c/mo\u003e\u003cmo\u003e+\u003c/mo\u003e\u003cmi\u003eEKOK\u003c/mi\u003e\u003cmo\u003e(\u003c/mo\u003e\u003cmn\u003e36\u003c/mn\u003e\u003cmo\u003e,\u003c/mo\u003e\u003cmn\u003e60\u003c/mn\u003e\u003cmo\u003e)\u003c/mo\u003e\u003c/mrow\u003e\u003c/math\u003e\u003c/p\u003e\",\"suggestedAnswer\":[{\"@type\":\"Answer\",\"text\":\"\u003cmath xmlns=\\\"http://www.w3.org/1998/Math/MathML\\\"\u003e\u003cmn\u003e192\u003c/mn\u003e\u003c/math\u003e\"},{\"@type\":\"Answer\",\"text\":\"\u003cmath xmlns=\\\"http://www.w3.org/1998/Math/MathML\\\"\u003e\u003cmn\u003e180\u003c/mn\u003e\u003c/math\u003e\"},{\"@type\":\"Answer\",\"text\":\"\u003cmath xmlns=\\\"http://www.w3.org/1998/Math/MathML\\\"\u003e\u003cmn\u003e168\u003c/mn\u003e\u003c/math\u003e\"},{\"@type\":\"Answer\",\"text\":\"\u003cmath xmlns=\\\"http://www.w3.org/1998/Math/MathML\\\"\u003e\u003cmn\u003e204\u003c/mn\u003e\u003c/math\u003e\"}]},{\"@type\":\"Question\",\"name\":\"\u003cp\u003ePozitif tam sayılar için\u003c/p\u003e\u003cp\u003e\u003cmath\u003e\u003cmtext\u003eEBOB\u003c/mtext\u003e\u003cmo\u003e(\u003c/mo\u003e\u003cmi\u003ea\u003c/mi\u003e\u003cmo\u003e,\u003c/mo\u003e\u003cmi\u003eb\u003c/mi\u003e\u003cmo\u003e)\u003c/mo\u003e\u003cmo\u003e=\u003c/mo\u003e\u003cmn\u003e18\u003c/mn\u003e\u003c/math\u003e, 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kaçtır?\u003c/p\u003e\",\"suggestedAnswer\":[{\"@type\":\"Answer\",\"text\":\"\u003cmath\u003e\u003cmn\u003e90\u003c/mn\u003e\u003c/math\u003e\"},{\"@type\":\"Answer\",\"text\":\"\u003cmath\u003e\u003cmn\u003e72\u003c/mn\u003e\u003c/math\u003e\"},{\"@type\":\"Answer\",\"text\":\"\u003cmath\u003e\u003cmn\u003e120\u003c/mn\u003e\u003c/math\u003e\"},{\"@type\":\"Answer\",\"text\":\"\u003cmath\u003e\u003cmn\u003e360\u003c/mn\u003e\u003c/math\u003e\"}]},{\"@type\":\"Question\",\"name\":\"\u003cp\u003eAşağıdaki işlemin sonucu kaçtır?\u003c/p\u003e\u003cp\u003e\u003cmath\u003e\u003cmi\u003eEBOB\u003c/mi\u003e\u003cmo\u003e(\u003c/mo\u003e\u003cmn\u003e24\u003c/mn\u003e\u003cmo\u003e,\u003c/mo\u003e\u003cmn\u003e36\u003c/mn\u003e\u003cmo\u003e)\u003c/mo\u003e\u003cmo\u003e+\u003c/mo\u003e\u003cmi\u003eEKOK\u003c/mi\u003e\u003cmo\u003e(\u003c/mo\u003e\u003cmn\u003e24\u003c/mn\u003e\u003cmo\u003e,\u003c/mo\u003e\u003cmn\u003e36\u003c/mn\u003e\u003cmo\u003e)\u003c/mo\u003e\u003c/math\u003e\u003c/p\u003e\",\"suggestedAnswer\":[{\"@type\":\"Answer\",\"text\":\"\u003cmath\u003e\u003cmn\u003e72\u003c/mn\u003e\u003c/math\u003e\"},{\"@type\":\"Answer\",\"text\":\"\u003cmath\u003e\u003cmn\u003e96\u003c/mn\u003e\u003c/math\u003e\"},{\"@type\":\"Answer\",\"text\":\"\u003cmath\u003e\u003cmn\u003e84\u003c/mn\u003e\u003c/math\u003e\"},{\"@type\":\"Answer\",\"text\":\"\u003cmath\u003e\u003cmn\u003e60\u003c/mn\u003e\u003c/math\u003e\"}]},{\"@type\":\"Question\",\"name\":\"\u003cp\u003eAşağıda iki pozitif tam sayı için verilen bilgilere göre diğer sayıyı bulun.\u003c/p\u003e\u003cp\u003e\u003cmath xmlns=\\\"http://www.w3.org/1998/Math/MathML\\\"\u003e\u003cmrow\u003e\u003cmi\u003eEBOB\u003c/mi\u003e\u003cmo\u003e(\u003c/mo\u003e\u003cmi\u003ea\u003c/mi\u003e\u003cmo\u003e,\u003c/mo\u003e\u003cmi\u003eb\u003c/mi\u003e\u003cmo\u003e)\u003c/mo\u003e\u003cmo\u003e=\u003c/mo\u003e\u003cmn\u003e6\u003c/mn\u003e\u003c/mrow\u003e\u003c/math\u003e\u003c/p\u003e\u003cp\u003e\u003cmath xmlns=\\\"http://www.w3.org/1998/Math/MathML\\\"\u003e\u003cmrow\u003e\u003cmi\u003eEKOK\u003c/mi\u003e\u003cmo\u003e(\u003c/mo\u003e\u003cmi\u003ea\u003c/mi\u003e\u003cmo\u003e,\u003c/mo\u003e\u003cmi\u003eb\u003c/mi\u003e\u003cmo\u003e)\u003c/mo\u003e\u003cmo\u003e=\u003c/mo\u003e\u003cmn\u003e180\u003c/mn\u003e\u003c/mrow\u003e\u003c/math\u003e\u003c/p\u003e\u003cp\u003e\u003cmath xmlns=\\\"http://www.w3.org/1998/Math/MathML\\\"\u003e\u003cmrow\u003e\u003cmi\u003ea\u003c/mi\u003e\u003cmo\u003e=\u003c/mo\u003e\u003cmn\u003e30\u003c/mn\u003e\u003c/mrow\u003e\u003c/math\u003e\u003c/p\u003e\u003cp\u003e\u003cmath xmlns=\\\"http://www.w3.org/1998/Math/MathML\\\"\u003e\u003cmrow\u003e\u003cmi\u003eb\u003c/mi\u003e\u003cmo\u003e=\u003c/mo\u003e\u003cmo\u003e?\u003c/mo\u003e\u003c/mrow\u003e\u003c/math\u003e\u003c/p\u003e\",\"suggestedAnswer\":[{\"@type\":\"Answer\",\"text\":\"\u003cmath xmlns=\\\"http://www.w3.org/1998/Math/MathML\\\"\u003e\u003cmn\u003e24\u003c/mn\u003e\u003c/math\u003e\"},{\"@type\":\"Answer\",\"text\":\"\u003cmath xmlns=\\\"http://www.w3.org/1998/Math/MathML\\\"\u003e\u003cmn\u003e54\u003c/mn\u003e\u003c/math\u003e\"},{\"@type\":\"Answer\",\"text\":\"\u003cmath xmlns=\\\"http://www.w3.org/1998/Math/MathML\\\"\u003e\u003cmn\u003e42\u003c/mn\u003e\u003c/math\u003e\"},{\"@type\":\"Answer\",\"text\":\"\u003cmath xmlns=\\\"http://www.w3.org/1998/Math/MathML\\\"\u003e\u003cmn\u003e36\u003c/mn\u003e\u003c/math\u003e\"}]},{\"@type\":\"Question\",\"name\":\"\u003cp\u003eAşağıdaki sayılar için \u003cb\u003eEKOK\u003c/b\u003e değeri kaçtır?\u003c/p\u003e\u003cmath xmlns=\\\"http://www.w3.org/1998/Math/MathML\\\"\u003e\u003cmtext\u003eEKOK\u003c/mtext\u003e\u003cmo\u003e(\u003c/mo\u003e\u003cmn\u003e24\u003c/mn\u003e\u003cmo\u003e,\u003c/mo\u003e\u003cmn\u003e36\u003c/mn\u003e\u003cmo\u003e)\u003c/mo\u003e\u003c/math\u003e\",\"suggestedAnswer\":[{\"@type\":\"Answer\",\"text\":\"\u003cmath xmlns=\\\"http://www.w3.org/1998/Math/MathML\\\"\u003e\u003cmn\u003e72\u003c/mn\u003e\u003c/math\u003e\"},{\"@type\":\"Answer\",\"text\":\"\u003cmath xmlns=\\\"http://www.w3.org/1998/Math/MathML\\\"\u003e\u003cmn\u003e36\u003c/mn\u003e\u003c/math\u003e\"},{\"@type\":\"Answer\",\"text\":\"\u003cmath xmlns=\\\"http://www.w3.org/1998/Math/MathML\\\"\u003e\u003cmn\u003e12\u003c/mn\u003e\u003c/math\u003e\"},{\"@type\":\"Answer\",\"text\":\"\u003cmath xmlns=\\\"http://www.w3.org/1998/Math/MathML\\\"\u003e\u003cmn\u003e144\u003c/mn\u003e\u003c/math\u003e\"}]},{\"@type\":\"Question\",\"name\":\"\u003cdiv\u003ePozitif tamsayılar \u003cmath\u003e\u003cmi\u003ea\u003c/mi\u003e\u003c/math\u003e ve \u003cmath\u003e\u003cmi\u003eb\u003c/mi\u003e\u003c/math\u003e için \u003cmath\u003e\u003cmi\u003eEBOB\u003c/mi\u003e\u003cmfenced\u003e\u003cmi\u003ea\u003c/mi\u003e\u003cmo\u003e,\u003c/mo\u003e\u003cmi\u003eb\u003c/mi\u003e\u003c/mfenced\u003e\u003cmo\u003e=\u003c/mo\u003e\u003cmn\u003e24\u003c/mn\u003e\u003c/math\u003e ve \u003cmath\u003e\u003cmi\u003eEKOK\u003c/mi\u003e\u003cmfenced\u003e\u003cmi\u003ea\u003c/mi\u003e\u003cmo\u003e,\u003c/mo\u003e\u003cmi\u003eb\u003c/mi\u003e\u003c/mfenced\u003e\u003cmo\u003e=\u003c/mo\u003e\u003cmn\u003e1680\u003c/mn\u003e\u003c/math\u003e veriliyor. Ayrıca \u003cmath\u003e\u003cmi\u003ea\u003c/mi\u003e\u003cmo\u003e\u0026lt;\u003c/mo\u003e\u003cmi\u003eb\u003c/mi\u003e\u003c/math\u003e ve \u003cmath\u003e\u003cmn\u003e7\u003c/mn\u003e\u003cmo\u003e\u0026#x2223;\u003c/mo\u003e\u003cmi\u003ea\u003c/mi\u003e\u003c/math\u003e. Buna göre \u003cmath\u003e\u003cmi\u003eb\u003c/mi\u003e\u003c/math\u003e kaçtır?\u003c/div\u003e\",\"suggestedAnswer\":[{\"@type\":\"Answer\",\"text\":\"\u003cmath\u003e\u003cmn\u003e168\u003c/mn\u003e\u003c/math\u003e\"},{\"@type\":\"Answer\",\"text\":\"\u003cmath\u003e\u003cmn\u003e240\u003c/mn\u003e\u003c/math\u003e\"},{\"@type\":\"Answer\",\"text\":\"\u003cmath\u003e\u003cmn\u003e336\u003c/mn\u003e\u003c/math\u003e\"},{\"@type\":\"Answer\",\"text\":\"\u003cmath\u003e\u003cmn\u003e420\u003c/mn\u003e\u003c/math\u003e\"}]},{\"@type\":\"Question\",\"name\":\"\u003cp\u003e\u003cmath\u003e\u003cmi\u003eEBOB\u003c/mi\u003e\u003cmo\u003e=\u003c/mo\u003e\u003cmn\u003e12\u003c/mn\u003e\u003c/math\u003e ve \u003cmath\u003e\u003cmi\u003eEKOK\u003c/mi\u003e\u003cmo\u003e=\u003c/mo\u003e\u003cmn\u003e180\u003c/mn\u003e\u003c/math\u003e olan iki sayının biri \u003cmath\u003e\u003cmn\u003e60\u003c/mn\u003e\u003c/math\u003e ise diğeri kaçtır?\u003c/p\u003e\",\"suggestedAnswer\":[{\"@type\":\"Answer\",\"text\":\"\u003cmath\u003e\u003cmn\u003e24\u003c/mn\u003e\u003c/math\u003e\"},{\"@type\":\"Answer\",\"text\":\"\u003cmath\u003e\u003cmn\u003e30\u003c/mn\u003e\u003c/math\u003e\"},{\"@type\":\"Answer\",\"text\":\"\u003cmath\u003e\u003cmn\u003e36\u003c/mn\u003e\u003c/math\u003e\"},{\"@type\":\"Answer\",\"text\":\"\u003cmath\u003e\u003cmn\u003e48\u003c/mn\u003e\u003c/math\u003e\"}]},{\"@type\":\"Question\",\"name\":\"\u003cp\u003e\u003cmath\u003e\u003cmrow\u003e\u003cmi\u003ea\u003c/mi\u003e\u003c/mrow\u003e\u003c/math\u003e ve \u003cmath\u003e\u003cmrow\u003e\u003cmi\u003eb\u003c/mi\u003e\u003c/mrow\u003e\u003c/math\u003e pozitif tam sayıları için \u003cmath\u003e\u003cmrow\u003e\u003cmi\u003eEBOB\u003c/mi\u003e\u003cmo\u003e(\u003c/mo\u003e\u003cmi\u003ea\u003c/mi\u003e\u003cmo\u003e,\u003c/mo\u003e\u003cmi\u003eb\u003c/mi\u003e\u003cmo\u003e)\u003c/mo\u003e\u003cmo\u003e=\u003c/mo\u003e\u003cmn\u003e18\u003c/mn\u003e\u003c/mrow\u003e\u003c/math\u003e ve \u003cmath\u003e\u003cmrow\u003e\u003cmi\u003eEKOK\u003c/mi\u003e\u003cmo\u003e(\u003c/mo\u003e\u003cmi\u003ea\u003c/mi\u003e\u003cmo\u003e,\u003c/mo\u003e\u003cmi\u003eb\u003c/mi\u003e\u003cmo\u003e)\u003c/mo\u003e\u003cmo\u003e=\u003c/mo\u003e\u003cmn\u003e1260\u003c/mn\u003e\u003c/mrow\u003e\u003c/math\u003e veriliyor. Buna göre \u003cmath\u003e\u003cmrow\u003e\u003cmi\u003ea\u003c/mi\u003e\u003cmo\u003e+\u003c/mo\u003e\u003cmi\u003eb\u003c/mi\u003e\u003c/mrow\u003e\u003c/math\u003e ifadesinin alabileceği en küçük değer kaçtır?\u003c/p\u003e\",\"suggestedAnswer\":[{\"@type\":\"Answer\",\"text\":\"\u003cmath\u003e\u003cmn\u003e342\u003c/mn\u003e\u003c/math\u003e\"},{\"@type\":\"Answer\",\"text\":\"\u003cmath\u003e\u003cmn\u003e666\u003c/mn\u003e\u003c/math\u003e\"},{\"@type\":\"Answer\",\"text\":\"\u003cmath\u003e\u003cmn\u003e324\u003c/mn\u003e\u003c/math\u003e\"},{\"@type\":\"Answer\",\"text\":\"\u003cmath\u003e\u003cmn\u003e306\u003c/mn\u003e\u003c/math\u003e\"}]},{\"@type\":\"Question\",\"name\":\"\u003cp\u003e\u003cmath\u003e\u003cmrow\u003e\u003cmi\u003eEBOB\u003c/mi\u003e\u003cmo stretchy=\\\"false\\\"\u003e(\u003c/mo\u003e\u003cmn\u003e36\u003c/mn\u003e\u003cmo\u003e,\u003c/mo\u003e\u003cmn\u003e48\u003c/mn\u003e\u003cmo stretchy=\\\"false\\\"\u003e)\u003c/mo\u003e\u003cmo\u003e+\u003c/mo\u003e\u003cmi\u003eEKOK\u003c/mi\u003e\u003cmo stretchy=\\\"false\\\"\u003e(\u003c/mo\u003e\u003cmn\u003e36\u003c/mn\u003e\u003cmo\u003e,\u003c/mo\u003e\u003cmn\u003e48\u003c/mn\u003e\u003cmo stretchy=\\\"false\\\"\u003e)\u003c/mo\u003e\u003c/mrow\u003e\u003c/math\u003e işleminin sonucu kaçtır?\u003c/p\u003e\",\"suggestedAnswer\":[{\"@type\":\"Answer\",\"text\":\"\u003cmath\u003e\u003cmn\u003e156\u003c/mn\u003e\u003c/math\u003e\"},{\"@type\":\"Answer\",\"text\":\"\u003cmath\u003e\u003cmn\u003e132\u003c/mn\u003e\u003c/math\u003e\"},{\"@type\":\"Answer\",\"text\":\"\u003cmath\u003e\u003cmn\u003e168\u003c/mn\u003e\u003c/math\u003e\"},{\"@type\":\"Answer\",\"text\":\"\u003cmath\u003e\u003cmn\u003e180\u003c/mn\u003e\u003c/math\u003e\"}]},{\"@type\":\"Question\",\"name\":\"\u003cp\u003e\u003cmath\u003e\u003cmrow\u003e\u003cmi\u003ea\u003c/mi\u003e\u003cmo\u003e,\u003c/mo\u003e\u003cmi\u003eb\u003c/mi\u003e\u003c/mrow\u003e\u003c/math\u003e doğal sayıları için \u003cmath\u003e\u003cmrow\u003e\u003cmtext\u003eEBOB\u003c/mtext\u003e\u003cmo\u003e(\u003c/mo\u003e\u003cmi\u003ea\u003c/mi\u003e\u003cmo\u003e,\u003c/mo\u003e\u003cmi\u003eb\u003c/mi\u003e\u003cmo\u003e)\u003c/mo\u003e\u003cmo\u003e=\u003c/mo\u003e\u003cmn\u003e18\u003c/mn\u003e\u003c/mrow\u003e\u003c/math\u003e ve \u003cmath\u003e\u003cmrow\u003e\u003cmtext\u003eEKOK\u003c/mtext\u003e\u003cmo\u003e(\u003c/mo\u003e\u003cmi\u003ea\u003c/mi\u003e\u003cmo\u003e,\u003c/mo\u003e\u003cmi\u003eb\u003c/mi\u003e\u003cmo\u003e)\u003c/mo\u003e\u003cmo\u003e=\u003c/mo\u003e\u003cmn\u003e540\u003c/mn\u003e\u003c/mrow\u003e\u003c/math\u003e olsun. Ayrıca \u003cmath\u003e\u003cmi\u003ea\u003c/mi\u003e\u003c/math\u003e sayısı \u003cmath\u003e\u003cmn\u003e90\u003c/mn\u003e\u003c/math\u003e ile tam bölünüyor ve \u003cmath\u003e\u003cmrow\u003e\u003cmi\u003ea\u003c/mi\u003e\u003cmo\u003e\u0026lt;\u003c/mo\u003e\u003cmi\u003eb\u003c/mi\u003e\u003c/mrow\u003e\u003c/math\u003e.\u003cbr/\u003eBuna göre \u003cmath\u003e\u003cmrow\u003e\u003cmi\u003eb\u003c/mi\u003e\u003cmo\u003e-\u003c/mo\u003e\u003cmi\u003ea\u003c/mi\u003e\u003c/mrow\u003e\u003c/math\u003e kaçtır?\u003c/p\u003e\",\"suggestedAnswer\":[{\"@type\":\"Answer\",\"text\":\"\u003cmath\u003e\u003cmn\u003e126\u003c/mn\u003e\u003c/math\u003e\"},{\"@type\":\"Answer\",\"text\":\"\u003cmath\u003e\u003cmn\u003e18\u003c/mn\u003e\u003c/math\u003e\"},{\"@type\":\"Answer\",\"text\":\"\u003cmath\u003e\u003cmn\u003e234\u003c/mn\u003e\u003c/math\u003e\"},{\"@type\":\"Answer\",\"text\":\"\u003cmath\u003e\u003cmn\u003e522\u003c/mn\u003e\u003c/math\u003e\"}]}]}"]) self.__next_f.push([1,"1a:T7a0,overflow-x-auto rounded-lg border border-slate-200 bg-white p-4 text-slate-700 shadow-sm shadow-slate-950/5 sm:p-5 [\u0026_h2:first-child]:mt-0 [\u0026_h2]:mt-2 [\u0026_h2]:scroll-mt-24 [\u0026_h2]:font-display [\u0026_h2]:text-2xl [\u0026_h2]:font-bold [\u0026_h2]:leading-tight [\u0026_h2]:text-slate-950 sm:[\u0026_h2]:text-3xl [\u0026_h3]:mt-5 [\u0026_h3]:scroll-mt-24 [\u0026_h3]:text-lg [\u0026_h3]:font-bold [\u0026_h3]:text-slate-950 [\u0026_li]:pl-1 [\u0026_li]:text-base [\u0026_li]:leading-7 [\u0026_p]:mt-3 [\u0026_p]:text-base [\u0026_p]:leading-7 [\u0026_p]:text-slate-700 [\u0026_strong]:font-bold [\u0026_strong]:text-slate-950 [\u0026_table]:mt-4 [\u0026_table]:min-w-[720px] [\u0026_table]:w-full [\u0026_table]:border-separate [\u0026_table]:border-spacing-0 [\u0026_table]:overflow-hidden [\u0026_table]:rounded-lg [\u0026_table]:border [\u0026_table]:border-slate-200 [\u0026_table]:text-sm [\u0026_tbody_tr:nth-child(even)]:bg-slate-50/70 [\u0026_td]:border-b [\u0026_td]:border-slate-100 [\u0026_td]:px-4 [\u0026_td]:py-3 [\u0026_td]:align-top [\u0026_td]:leading-6 [\u0026_td]:text-slate-700 [\u0026_td]:whitespace-normal [\u0026_td]:break-words [\u0026_th]:border-b [\u0026_th]:border-slate-200 [\u0026_th]:bg-slate-100 [\u0026_th]:px-4 [\u0026_th]:py-2.5 [\u0026_th]:text-left [\u0026_th]:align-bottom [\u0026_th]:text-xs [\u0026_th]:font-bold [\u0026_th]:uppercase [\u0026_th]:tracking-wide [\u0026_th]:text-slate-600 [\u0026_ul]:mt-4 [\u0026_ul]:list-disc [\u0026_ul]:space-y-1.5 [\u0026_ul]:pl-6 max-sm:[\u0026_table]:block max-sm:[\u0026_table]:min-w-0 max-sm:[\u0026_table]:border-0 max-sm:[\u0026_table]:bg-transparent max-sm:[\u0026_thead]:hidden max-sm:[\u0026_tbody]:block max-sm:[\u0026_tr]:mb-2.5 max-sm:[\u0026_tr]:block max-sm:[\u0026_tr]:overflow-hidden max-sm:[\u0026_tr]:rounded-lg max-sm:[\u0026_tr]:border max-sm:[\u0026_tr]:border-slate-200 max-sm:[\u0026_tr]:bg-white max-sm:[\u0026_tr]:shadow-sm max-sm:[\u0026_td]:grid max-sm:[\u0026_td]:grid-cols-[minmax(7rem,0.42fr)_minmax(0,1fr)] max-sm:[\u0026_td]:gap-3 max-sm:[\u0026_td]:px-4 max-sm:[\u0026_td]:py-2.5 max-sm:[\u0026_td]:text-sm max-sm:[\u0026_td]:before:text-[11px] max-sm:[\u0026_td]:before:font-bold max-sm:[\u0026_td]:before:uppercase max-sm:[\u0026_td]:before:tracking-wide max-sm:[\u0026_td]:before:text-slate-500 max-sm:[\u0026_td]:before:content-[attr(data-label)]1c:T8a3,"]) self.__next_f.push([1,"\u003cdiv style='text-align:left; margin-bottom:14px;'\u003e\u003cp style='margin:0 0 10px 0;'\u003eİfadede iki sayı için EBOB ve EKOK isteniyor.\u003c/p\u003e\u003cmath display='block' xmlns='http://www.w3.org/1998/Math/MathML'\u003e\u003cmrow\u003e\u003cmi\u003ea\u003c/mi\u003e\u003cmo\u003e=\u003c/mo\u003e\u003cmn\u003e36\u003c/mn\u003e\u003cmo\u003e,\u003c/mo\u003e\u003cmspace width='0.6em'/\u003e\u003cmi\u003eb\u003c/mi\u003e\u003cmo\u003e=\u003c/mo\u003e\u003cmn\u003e60\u003c/mn\u003e\u003c/mrow\u003e\u003c/math\u003e\u003c/div\u003e\u003cdiv style='text-align:left; margin-bottom:14px;'\u003e\u003cp style='margin:0 0 10px 0;'\u003eÖnce asal çarpanlarına ayıralım.\u003c/p\u003e\u003cmath display='block' xmlns='http://www.w3.org/1998/Math/MathML'\u003e\u003cmrow\u003e\u003cmn\u003e36\u003c/mn\u003e\u003cmo\u003e=\u003c/mo\u003e\u003cmsup\u003e\u003cmn\u003e2\u003c/mn\u003e\u003cmn\u003e2\u003c/mn\u003e\u003c/msup\u003e\u003cmo\u003e\u0026#x00D7;\u003c/mo\u003e\u003cmsup\u003e\u003cmn\u003e3\u003c/mn\u003e\u003cmn\u003e2\u003c/mn\u003e\u003c/msup\u003e\u003c/mrow\u003e\u003c/math\u003e\u003cmath display='block' xmlns='http://www.w3.org/1998/Math/MathML'\u003e\u003cmrow\u003e\u003cmn\u003e60\u003c/mn\u003e\u003cmo\u003e=\u003c/mo\u003e\u003cmsup\u003e\u003cmn\u003e2\u003c/mn\u003e\u003cmn\u003e2\u003c/mn\u003e\u003c/msup\u003e\u003cmo\u003e\u0026#x00D7;\u003c/mo\u003e\u003cmn\u003e3\u003c/mn\u003e\u003cmo\u003e\u0026#x00D7;\u003c/mo\u003e\u003cmn\u003e5\u003c/mn\u003e\u003c/mrow\u003e\u003c/math\u003e\u003c/div\u003e\u003cdiv style='text-align:left; margin-bottom:14px;'\u003e\u003cp style='margin:0 0 10px 0;'\u003eEBOB: ortak asal çarpanların küçük üsleri alınır.\u003c/p\u003e\u003cmath display='block' xmlns='http://www.w3.org/1998/Math/MathML'\u003e\u003cmrow\u003e\u003cmi\u003eEBOB\u003c/mi\u003e\u003cmo\u003e(\u003c/mo\u003e\u003cmn\u003e36\u003c/mn\u003e\u003cmo\u003e,\u003c/mo\u003e\u003cmn\u003e60\u003c/mn\u003e\u003cmo\u003e)\u003c/mo\u003e\u003cmo\u003e=\u003c/mo\u003e\u003cmsup\u003e\u003cmn\u003e2\u003c/mn\u003e\u003cmn\u003e2\u003c/mn\u003e\u003c/msup\u003e\u003cmo\u003e\u0026#x00D7;\u003c/mo\u003e\u003cmn\u003e3\u003c/mn\u003e\u003cmo\u003e=\u003c/mo\u003e\u003cmn\u003e12\u003c/mn\u003e\u003c/mrow\u003e\u003c/math\u003e\u003c/div\u003e\u003cdiv style='text-align:left; margin-bottom:14px;'\u003e\u003cp style='margin:0 0 10px 0;'\u003eEKOK: asal çarpanların büyük üsleri alınır.\u003c/p\u003e\u003cmath display='block' xmlns='http://www.w3.org/1998/Math/MathML'\u003e\u003cmrow\u003e\u003cmi\u003eEKOK\u003c/mi\u003e\u003cmo\u003e(\u003c/mo\u003e\u003cmn\u003e36\u003c/mn\u003e\u003cmo\u003e,\u003c/mo\u003e\u003cmn\u003e60\u003c/mn\u003e\u003cmo\u003e)\u003c/mo\u003e\u003cmo\u003e=\u003c/mo\u003e\u003cmsup\u003e\u003cmn\u003e2\u003c/mn\u003e\u003cmn\u003e2\u003c/mn\u003e\u003c/msup\u003e\u003cmo\u003e\u0026#x00D7;\u003c/mo\u003e\u003cmsup\u003e\u003cmn\u003e3\u003c/mn\u003e\u003cmn\u003e2\u003c/mn\u003e\u003c/msup\u003e\u003cmo\u003e\u0026#x00D7;\u003c/mo\u003e\u003cmn\u003e5\u003c/mn\u003e\u003cmo\u003e=\u003c/mo\u003e\u003cmn\u003e180\u003c/mn\u003e\u003c/mrow\u003e\u003c/math\u003e\u003c/div\u003e\u003cdiv style='text-align:left; margin-bottom:14px;'\u003e\u003cp style='margin:0 0 10px 0;'\u003eİstenen toplamı bulalım.\u003c/p\u003e\u003cmath display='block' xmlns='http://www.w3.org/1998/Math/MathML'\u003e\u003cmrow\u003e\u003cmi\u003eEBOB\u003c/mi\u003e\u003cmo\u003e(\u003c/mo\u003e\u003cmn\u003e36\u003c/mn\u003e\u003cmo\u003e,\u003c/mo\u003e\u003cmn\u003e60\u003c/mn\u003e\u003cmo\u003e)\u003c/mo\u003e\u003cmo\u003e+\u003c/mo\u003e\u003cmi\u003eEKOK\u003c/mi\u003e\u003cmo\u003e(\u003c/mo\u003e\u003cmn\u003e36\u003c/mn\u003e\u003cmo\u003e,\u003c/mo\u003e\u003cmn\u003e60\u003c/mn\u003e\u003cmo\u003e)\u003c/mo\u003e\u003cmo\u003e=\u003c/mo\u003e\u003cmn\u003e12\u003c/mn\u003e\u003cmo\u003e+\u003c/mo\u003e\u003cmn\u003e180\u003c/mn\u003e\u003cmo\u003e=\u003c/mo\u003e\u003cmn\u003e192\u003c/mn\u003e\u003c/mrow\u003e\u003c/math\u003e\u003c/div\u003e\u003cdiv style='text-align:left; margin-bottom:0px;'\u003e\u003cp style='margin:0;'\u003eSonuç \u003cspan\u003e192\u003c/span\u003e olduğundan doğru cevap \u003cspan\u003eC\u003c/span\u003e şıkkıdır.\u003c/p\u003e\u003c/div\u003e"]) self.__next_f.push([1,"1d:Tfb7,"]) self.__next_f.push([1,"\u003cdiv style=\"text-align:left; margin-bottom:12px;\"\u003e\u003cp style=\"margin:0 0 12px 0;\"\u003eVerilenler:\u003c/p\u003e\u003cmath display=\"block\"\u003e\u003cmtext\u003eEBOB\u003c/mtext\u003e\u003cmo\u003e(\u003c/mo\u003e\u003cmi\u003ea\u003c/mi\u003e\u003cmo\u003e,\u003c/mo\u003e\u003cmi\u003eb\u003c/mi\u003e\u003cmo\u003e)\u003c/mo\u003e\u003cmo\u003e=\u003c/mo\u003e\u003cmn\u003e18\u003c/mn\u003e\u003c/math\u003e\u003cmath display=\"block\"\u003e\u003cmtext\u003eEKOK\u003c/mtext\u003e\u003cmo\u003e(\u003c/mo\u003e\u003cmi\u003ea\u003c/mi\u003e\u003cmo\u003e,\u003c/mo\u003e\u003cmi\u003eb\u003c/mi\u003e\u003cmo\u003e)\u003c/mo\u003e\u003cmo\u003e=\u003c/mo\u003e\u003cmn\u003e360\u003c/mn\u003e\u003c/math\u003e\u003cmath display=\"block\"\u003e\u003cmn\u003e24\u003c/mn\u003e\u003cmo\u003e|\u003c/mo\u003e\u003cmi\u003ea\u003c/mi\u003e\u003c/math\u003e\u003cmath display=\"block\"\u003e\u003cmi\u003ea\u003c/mi\u003e\u003cmo\u003e\u0026lt;\u003c/mo\u003e\u003cmi\u003eb\u003c/mi\u003e\u003c/math\u003e\u003c/div\u003e\u003cdiv style=\"text-align:left; margin-bottom:12px;\"\u003e\u003cp style=\"margin:0 0 12px 0;\"\u003eEBOB ve EKOK ilişkisini kullanalım:\u003c/p\u003e\u003cmath display=\"block\"\u003e\u003cmi\u003ea\u003c/mi\u003e\u003cmi\u003eb\u003c/mi\u003e\u003cmo\u003e=\u003c/mo\u003e\u003cmtext\u003eEBOB\u003c/mtext\u003e\u003cmo\u003e(\u003c/mo\u003e\u003cmi\u003ea\u003c/mi\u003e\u003cmo\u003e,\u003c/mo\u003e\u003cmi\u003eb\u003c/mi\u003e\u003cmo\u003e)\u003c/mo\u003e\u003cmo\u003e\u0026#x00D7;\u003c/mo\u003e\u003cmtext\u003eEKOK\u003c/mtext\u003e\u003cmo\u003e(\u003c/mo\u003e\u003cmi\u003ea\u003c/mi\u003e\u003cmo\u003e,\u003c/mo\u003e\u003cmi\u003eb\u003c/mi\u003e\u003cmo\u003e)\u003c/mo\u003e\u003c/math\u003e\u003cmath display=\"block\"\u003e\u003cmi\u003ea\u003c/mi\u003e\u003cmi\u003eb\u003c/mi\u003e\u003cmo\u003e=\u003c/mo\u003e\u003cmn\u003e18\u003c/mn\u003e\u003cmo\u003e\u0026#x00D7;\u003c/mo\u003e\u003cmn\u003e360\u003c/mn\u003e\u003cmo\u003e=\u003c/mo\u003e\u003cmn\u003e6480\u003c/mn\u003e\u003c/math\u003e\u003c/div\u003e\u003cdiv style=\"text-align:left; margin-bottom:12px;\"\u003e\u003cp style=\"margin:0 0 12px 0;\"\u003eEBOB 18 olduğuna göre sayıları 18 çarpanı ile yazalım:\u003c/p\u003e\u003cmath display=\"block\"\u003e\u003cmi\u003ea\u003c/mi\u003e\u003cmo\u003e=\u003c/mo\u003e\u003cmn\u003e18\u003c/mn\u003e\u003cmi\u003ex\u003c/mi\u003e\u003c/math\u003e\u003cmath display=\"block\"\u003e\u003cmi\u003eb\u003c/mi\u003e\u003cmo\u003e=\u003c/mo\u003e\u003cmn\u003e18\u003c/mn\u003e\u003cmi\u003ey\u003c/mi\u003e\u003c/math\u003e\u003cp style=\"margin:0 0 12px 0;\"\u003eBurada\u003c/p\u003e\u003cmath display=\"block\"\u003e\u003cmtext\u003eEBOB\u003c/mtext\u003e\u003cmo\u003e(\u003c/mo\u003e\u003cmi\u003ex\u003c/mi\u003e\u003cmo\u003e,\u003c/mo\u003e\u003cmi\u003ey\u003c/mi\u003e\u003cmo\u003e)\u003c/mo\u003e\u003cmo\u003e=\u003c/mo\u003e\u003cmn\u003e1\u003c/mn\u003e\u003c/math\u003e\u003c/div\u003e\u003cdiv style=\"text-align:left; margin-bottom:12px;\"\u003e\u003cp style=\"margin:0 0 12px 0;\"\u003eEKOK koşulunu yazalım. EBOB 1 olduğu için\u003c/p\u003e\u003cmath display=\"block\"\u003e\u003cmtext\u003eEKOK\u003c/mtext\u003e\u003cmo\u003e(\u003c/mo\u003e\u003cmi\u003ex\u003c/mi\u003e\u003cmo\u003e,\u003c/mo\u003e\u003cmi\u003ey\u003c/mi\u003e\u003cmo\u003e)\u003c/mo\u003e\u003cmo\u003e=\u003c/mo\u003e\u003cmi\u003ex\u003c/mi\u003e\u003cmi\u003ey\u003c/mi\u003e\u003c/math\u003e\u003cp style=\"margin:0 0 12px 0;\"\u003eDolayısıyla\u003c/p\u003e\u003cmath display=\"block\"\u003e\u003cmtext\u003eEKOK\u003c/mtext\u003e\u003cmo\u003e(\u003c/mo\u003e\u003cmi\u003ea\u003c/mi\u003e\u003cmo\u003e,\u003c/mo\u003e\u003cmi\u003eb\u003c/mi\u003e\u003cmo\u003e)\u003c/mo\u003e\u003cmo\u003e=\u003c/mo\u003e\u003cmn\u003e18\u003c/mn\u003e\u003cmi\u003ex\u003c/mi\u003e\u003cmi\u003ey\u003c/mi\u003e\u003cmo\u003e=\u003c/mo\u003e\u003cmn\u003e360\u003c/mn\u003e\u003c/math\u003e\u003cmath display=\"block\"\u003e\u003cmi\u003ex\u003c/mi\u003e\u003cmi\u003ey\u003c/mi\u003e\u003cmo\u003e=\u003c/mo\u003e\u003cmn\u003e20\u003c/mn\u003e\u003c/math\u003e\u003c/div\u003e\u003cdiv style=\"text-align:left; margin-bottom:12px;\"\u003e\u003cp style=\"margin:0 0 12px 0;\"\u003eÇarpımı 20 olan ve aralarında asal olan ikililer:\u003c/p\u003e\u003cmath display=\"block\"\u003e\u003cmo\u003e(\u003c/mo\u003e\u003cmi\u003ex\u003c/mi\u003e\u003cmo\u003e,\u003c/mo\u003e\u003cmi\u003ey\u003c/mi\u003e\u003cmo\u003e)\u003c/mo\u003e\u003cmo\u003e=\u003c/mo\u003e\u003cmo\u003e(\u003c/mo\u003e\u003cmn\u003e1\u003c/mn\u003e\u003cmo\u003e,\u003c/mo\u003e\u003cmn\u003e20\u003c/mn\u003e\u003cmo\u003e)\u003c/mo\u003e\u003c/math\u003e\u003cmath display=\"block\"\u003e\u003cmo\u003e(\u003c/mo\u003e\u003cmi\u003ex\u003c/mi\u003e\u003cmo\u003e,\u003c/mo\u003e\u003cmi\u003ey\u003c/mi\u003e\u003cmo\u003e)\u003c/mo\u003e\u003cmo\u003e=\u003c/mo\u003e\u003cmo\u003e(\u003c/mo\u003e\u003cmn\u003e4\u003c/mn\u003e\u003cmo\u003e,\u003c/mo\u003e\u003cmn\u003e5\u003c/mn\u003e\u003cmo\u003e)\u003c/mo\u003e\u003c/math\u003e\u003cp style=\"margin:0 0 12px 0;\"\u003eAyrıca\u003c/p\u003e\u003cmath display=\"block\"\u003e\u003cmi\u003ea\u003c/mi\u003e\u003cmo\u003e\u0026lt;\u003c/mo\u003e\u003cmi\u003eb\u003c/mi\u003e\u003c/math\u003e\u003cp style=\"margin:0 0 12px 0;\"\u003eolduğu için\u003c/p\u003e\u003cmath display=\"block\"\u003e\u003cmi\u003ex\u003c/mi\u003e\u003cmo\u003e\u0026lt;\u003c/mo\u003e\u003cmi\u003ey\u003c/mi\u003e\u003c/math\u003e\u003c/div\u003e\u003cdiv style=\"text-align:left; margin-bottom:12px;\"\u003e\u003cp style=\"margin:0 0 12px 0;\"\u003eŞimdi 24 bölünebilme koşulunu kullanalım:\u003c/p\u003e\u003cmath display=\"block\"\u003e\u003cmn\u003e24\u003c/mn\u003e\u003cmo\u003e|\u003c/mo\u003e\u003cmi\u003ea\u003c/mi\u003e\u003c/math\u003e\u003cmath display=\"block\"\u003e\u003cmn\u003e24\u003c/mn\u003e\u003cmo\u003e|\u003c/mo\u003e\u003cmn\u003e18\u003c/mn\u003e\u003cmi\u003ex\u003c/mi\u003e\u003c/math\u003e\u003cp style=\"margin:0 0 12px 0;\"\u003eBu,\u003c/p\u003e\u003cmath display=\"block\"\u003e\u003cmn\u003e18\u003c/mn\u003e\u003cmi\u003ex\u003c/mi\u003e\u003cmo\u003e=\u003c/mo\u003e\u003cmn\u003e24\u003c/mn\u003e\u003cmi\u003ek\u003c/mi\u003e\u003c/math\u003e\u003cp style=\"margin:0 0 12px 0;\"\u003eşeklinde yazılabilir. Buradan\u003c/p\u003e\u003cmath display=\"block\"\u003e\u003cmi\u003ex\u003c/mi\u003e\u003cmo\u003e=\u003c/mo\u003e\u003cmfrac\u003e\u003cmn\u003e24\u003c/mn\u003e\u003cmn\u003e18\u003c/mn\u003e\u003c/mfrac\u003e\u003cmi\u003ek\u003c/mi\u003e\u003cmo\u003e=\u003c/mo\u003e\u003cmfrac\u003e\u003cmn\u003e4\u003c/mn\u003e\u003cmn\u003e3\u003c/mn\u003e\u003c/mfrac\u003e\u003cmi\u003ek\u003c/mi\u003e\u003c/math\u003e\u003cp style=\"margin:0 0 12px 0;\"\u003ex tam sayı olacağı için\u003c/p\u003e\u003cmath display=\"block\"\u003e\u003cmn\u003e3\u003c/mn\u003e\u003cmo\u003e|\u003c/mo\u003e\u003cmi\u003ek\u003c/mi\u003e\u003c/math\u003e\u003cp style=\"margin:0 0 12px 0;\"\u003eolmalı; yani x en az 4’ün katı olmak zorundadır. Listede bu şartı sağlayan tek seçenek\u003c/p\u003e\u003cmath display=\"block\"\u003e\u003cmi\u003ex\u003c/mi\u003e\u003cmo\u003e=\u003c/mo\u003e\u003cmn\u003e4\u003c/mn\u003e\u003c/math\u003e\u003cp style=\"margin:0 0 12px 0;\"\u003eolur ve buna karşılık\u003c/p\u003e\u003cmath display=\"block\"\u003e\u003cmi\u003ey\u003c/mi\u003e\u003cmo\u003e=\u003c/mo\u003e\u003cmn\u003e5\u003c/mn\u003e\u003c/math\u003e\u003c/div\u003e\u003cdiv style=\"text-align:left; margin-bottom:12px;\"\u003e\u003cp style=\"margin:0 0 12px 0;\"\u003eSonuç:\u003c/p\u003e\u003cmath display=\"block\"\u003e\u003cmi\u003ea\u003c/mi\u003e\u003cmo\u003e=\u003c/mo\u003e\u003cmn\u003e18\u003c/mn\u003e\u003cmo\u003e\u0026#x00D7;\u003c/mo\u003e\u003cmn\u003e4\u003c/mn\u003e\u003cmo\u003e=\u003c/mo\u003e\u003cmn\u003e72\u003c/mn\u003e\u003c/math\u003e\u003c/div\u003e\u003cdiv style=\"text-align:left; margin-bottom:0;\"\u003e\u003cp style=\"margin:0 0 12px 0;\"\u003eDoğru seçenek kontrolü:\u003c/p\u003e\u003cmath display=\"block\"\u003e\u003cmn\u003e72\u003c/mn\u003e\u003c/math\u003e\u003cp style=\"margin:0;\"\u003eBu değer şıklarda B seçeneğidir; yani doğru cevap B’dir.\u003c/p\u003e\u003c/div\u003e"]) self.__next_f.push([1,"1e:T62f,\u003cdiv style=\"text-align:left;\"\u003e\u003cp style=\"margin:0 0 12px 0;\"\u003eİstenen ifade:\u003c/p\u003e\u003cmath display=\"block\"\u003e\u003cmrow\u003e\u003cmi\u003eEBOB\u003c/mi\u003e\u003cmo\u003e(\u003c/mo\u003e\u003cmn\u003e24\u003c/mn\u003e\u003cmo\u003e,\u003c/mo\u003e\u003cmn\u003e36\u003c/mn\u003e\u003cmo\u003e)\u003c/mo\u003e\u003cmo\u003e+\u003c/mo\u003e\u003cmi\u003eEKOK\u003c/mi\u003e\u003cmo\u003e(\u003c/mo\u003e\u003cmn\u003e24\u003c/mn\u003e\u003cmo\u003e,\u003c/mo\u003e\u003cmn\u003e36\u003c/mn\u003e\u003cmo\u003e)\u003c/mo\u003e\u003c/mrow\u003e\u003c/math\u003e\u003cp style=\"margin:0 0 12px 0;\"\u003eÖnce sayıları asal çarpanlarına ayıralım:\u003c/p\u003e\u003cmath display=\"block\"\u003e\u003cmrow\u003e\u003cmn\u003e24\u003c/mn\u003e\u003cmo\u003e=\u003c/mo\u003e\u003cmsup\u003e\u003cmn\u003e2\u003c/mn\u003e\u003cmn\u003e3\u003c/mn\u003e\u003c/msup\u003e\u003cmo\u003e·\u003c/mo\u003e\u003cmn\u003e3\u003c/mn\u003e\u003c/mrow\u003e\u003c/math\u003e\u003cmath display=\"block\"\u003e\u003cmrow\u003e\u003cmn\u003e36\u003c/mn\u003e\u003cmo\u003e=\u003c/mo\u003e\u003cmsup\u003e\u003cmn\u003e2\u003c/mn\u003e\u003cmn\u003e2\u003c/mn\u003e\u003c/msup\u003e\u003cmo\u003e·\u003c/mo\u003e\u003cmsup\u003e\u003cmn\u003e3\u003c/mn\u003e\u003cmn\u003e2\u003c/mn\u003e\u003c/msup\u003e\u003c/mrow\u003e\u003c/math\u003e\u003cp style=\"margin:0 0 12px 0;\"\u003eEBOB için ortak asal çarpanların üslerinin küçüğünü alırız:\u003c/p\u003e\u003cmath display=\"block\"\u003e\u003cmrow\u003e\u003cmi\u003eEBOB\u003c/mi\u003e\u003cmo\u003e(\u003c/mo\u003e\u003cmn\u003e24\u003c/mn\u003e\u003cmo\u003e,\u003c/mo\u003e\u003cmn\u003e36\u003c/mn\u003e\u003cmo\u003e)\u003c/mo\u003e\u003cmo\u003e=\u003c/mo\u003e\u003cmsup\u003e\u003cmn\u003e2\u003c/mn\u003e\u003cmn\u003e2\u003c/mn\u003e\u003c/msup\u003e\u003cmo\u003e·\u003c/mo\u003e\u003cmsup\u003e\u003cmn\u003e3\u003c/mn\u003e\u003cmn\u003e1\u003c/mn\u003e\u003c/msup\u003e\u003cmo\u003e=\u003c/mo\u003e\u003cmn\u003e12\u003c/mn\u003e\u003c/mrow\u003e\u003c/math\u003e\u003cp style=\"margin:0 0 12px 0;\"\u003eEKOK için asal çarpanların üslerinin büyüğünü alırız:\u003c/p\u003e\u003cmath display=\"block\"\u003e\u003cmrow\u003e\u003cmi\u003eEKOK\u003c/mi\u003e\u003cmo\u003e(\u003c/mo\u003e\u003cmn\u003e24\u003c/mn\u003e\u003cmo\u003e,\u003c/mo\u003e\u003cmn\u003e36\u003c/mn\u003e\u003cmo\u003e)\u003c/mo\u003e\u003cmo\u003e=\u003c/mo\u003e\u003cmsup\u003e\u003cmn\u003e2\u003c/mn\u003e\u003cmn\u003e3\u003c/mn\u003e\u003c/msup\u003e\u003cmo\u003e·\u003c/mo\u003e\u003cmsup\u003e\u003cmn\u003e3\u003c/mn\u003e\u003cmn\u003e2\u003c/mn\u003e\u003c/msup\u003e\u003cmo\u003e=\u003c/mo\u003e\u003cmn\u003e72\u003c/mn\u003e\u003c/mrow\u003e\u003c/math\u003e\u003cp style=\"margin:0 0 12px 0;\"\u003eToplayalım:\u003c/p\u003e\u003cmath display=\"block\"\u003e\u003cmrow\u003e\u003cmi\u003eEBOB\u003c/mi\u003e\u003cmo\u003e(\u003c/mo\u003e\u003cmn\u003e24\u003c/mn\u003e\u003cmo\u003e,\u003c/mo\u003e\u003cmn\u003e36\u003c/mn\u003e\u003cmo\u003e)\u003c/mo\u003e\u003cmo\u003e+\u003c/mo\u003e\u003cmi\u003eEKOK\u003c/mi\u003e\u003cmo\u003e(\u003c/mo\u003e\u003cmn\u003e24\u003c/mn\u003e\u003cmo\u003e,\u003c/mo\u003e\u003cmn\u003e36\u003c/mn\u003e\u003cmo\u003e)\u003c/mo\u003e\u003cmo\u003e=\u003c/mo\u003e\u003cmn\u003e12\u003c/mn\u003e\u003cmo\u003e+\u003c/mo\u003e\u003cmn\u003e72\u003c/mn\u003e\u003cmo\u003e=\u003c/mo\u003e\u003cmn\u003e84\u003c/mn\u003e\u003c/mrow\u003e\u003c/math\u003e\u003cp style=\"margin:0 0 0 0;\"\u003eDoğru seçenek: C1515\u003c/p\u003e\u003c/div\u003e1f:T74a,\u003cdiv style=\"text-align:left; margin-bottom:12px;\"\u003e\u003cp style=\"margin:0 0 12px 0;\"\u003eDoğru seçenek \u003cb\u003eB\u003c/b\u003e’dir.\u003c/p\u003e\u003c/div\u003e\u003cdiv style=\"text-align:left; margin-bottom:12px;\"\u003e\u003cp style=\"margin:0 0 12px 0;\"\u003eİki pozitif tam sayı için temel bağıntı:\u003c/p\u003e\u003cmath xmlns=\"http://www.w3.org/1998/Math/MathML\" display=\"block\"\u003e\u003cmrow\u003e\u003cmi\u003eEBOB\u003c/mi\u003e\u003cmo\u003e(\u003c/mo\u003e\u003cmi\u003ea\u003c/mi\u003e\u003cmo\u003e,\u003c/mo\u003e\u003cmi\u003eb\u003c/mi\u003e\u003cmo\u003e)\u003c/mo\u003e\u003cmo\u003e\u0026#x22C5;\u003c/mo\u003e\u003cmi\u003eEKOK\u003c/mi\u003e\u003cmo\u003e(\u003c/mo\u003e\u003cmi\u003ea\u003c/mi\u003e\u003cmo\u003e,\u003c/mo\u003e\u003cmi\u003e"]) self.__next_f.push([1,"b\u003c/mi\u003e\u003cmo\u003e)\u003c/mo\u003e\u003cmo\u003e=\u003c/mo\u003e\u003cmi\u003ea\u003c/mi\u003e\u003cmo\u003e\u0026#x22C5;\u003c/mo\u003e\u003cmi\u003eb\u003c/mi\u003e\u003c/mrow\u003e\u003c/math\u003e\u003c/div\u003e\u003cdiv style=\"text-align:left; margin-bottom:12px;\"\u003e\u003cp style=\"margin:0 0 12px 0;\"\u003eVerilenleri yerine yazalım:\u003c/p\u003e\u003cmath xmlns=\"http://www.w3.org/1998/Math/MathML\" display=\"block\"\u003e\u003cmrow\u003e\u003cmn\u003e6\u003c/mn\u003e\u003cmo\u003e\u0026#x22C5;\u003c/mo\u003e\u003cmn\u003e180\u003c/mn\u003e\u003cmo\u003e=\u003c/mo\u003e\u003cmn\u003e30\u003c/mn\u003e\u003cmo\u003e\u0026#x22C5;\u003c/mo\u003e\u003cmi\u003eb\u003c/mi\u003e\u003c/mrow\u003e\u003c/math\u003e\u003c/div\u003e\u003cdiv style=\"text-align:left; margin-bottom:12px;\"\u003e\u003cp style=\"margin:0 0 12px 0;\"\u003eSol tarafı hesaplayalım:\u003c/p\u003e\u003cmath xmlns=\"http://www.w3.org/1998/Math/MathML\" display=\"block\"\u003e\u003cmrow\u003e\u003cmn\u003e6\u003c/mn\u003e\u003cmo\u003e\u0026#x22C5;\u003c/mo\u003e\u003cmn\u003e180\u003c/mn\u003e\u003cmo\u003e=\u003c/mo\u003e\u003cmn\u003e1080\u003c/mn\u003e\u003c/mrow\u003e\u003c/math\u003e\u003c/div\u003e\u003cdiv style=\"text-align:left; margin-bottom:12px;\"\u003e\u003cp style=\"margin:0 0 12px 0;\"\u003eEşitliği düzenleyelim:\u003c/p\u003e\u003cmath xmlns=\"http://www.w3.org/1998/Math/MathML\" display=\"block\"\u003e\u003cmrow\u003e\u003cmn\u003e1080\u003c/mn\u003e\u003cmo\u003e=\u003c/mo\u003e\u003cmn\u003e30\u003c/mn\u003e\u003cmo\u003e\u0026#x22C5;\u003c/mo\u003e\u003cmi\u003eb\u003c/mi\u003e\u003c/mrow\u003e\u003c/math\u003e\u003c/div\u003e\u003cdiv style=\"text-align:left; margin-bottom:12px;\"\u003e\u003cp style=\"margin:0 0 12px 0;\"\u003eHer iki tarafı \u003cspan style=\"white-space:nowrap;\"\u003e30\u003c/span\u003e’a bölelim:\u003c/p\u003e\u003cmath xmlns=\"http://www.w3.org/1998/Math/MathML\" display=\"block\"\u003e\u003cmrow\u003e\u003cmi\u003eb\u003c/mi\u003e\u003cmo\u003e=\u003c/mo\u003e\u003cmfrac\u003e\u003cmn\u003e1080\u003c/mn\u003e\u003cmn\u003e30\u003c/mn\u003e\u003c/mfrac\u003e\u003c/mrow\u003e\u003c/math\u003e\u003c/div\u003e\u003cdiv style=\"text-align:left; margin-bottom:12px;\"\u003e\u003cp style=\"margin:0 0 12px 0;\"\u003eSonuç:\u003c/p\u003e\u003cmath xmlns=\"http://www.w3.org/1998/Math/MathML\" display=\"block\"\u003e\u003cmrow\u003e\u003cmi\u003eb\u003c/mi\u003e\u003cmo\u003e=\u003c/mo\u003e\u003cmn\u003e36\u003c/mn\u003e\u003c/mrow\u003e\u003c/math\u003e\u003c/div\u003e20:T72c,\u003cdiv style=\"text-align:left;margin-bottom:12px;\"\u003e\u003cp\u003eSoruda istenen değer, verilen iki sayının EKOK’udur. Şıkları kontrol etmek için EKOK’u asal çarpanlara ayırarak bulalım.\u003c/p\u003e\u003c/div\u003e\u003cdiv style=\"text-align:left;margin-bottom:12px;\"\u003e\u003cp\u003eVerilen sayılar:\u003c/p\u003e\u003cmath xmlns=\"http://www.w3.org/1998/Math/MathML\" display=\"block\"\u003e\u003cmrow\u003e\u003cmn\u003e24\u003c/mn\u003e\u003cmo\u003e,\u003c/mo\u003e\u003cmn\u003e36\u003c/mn\u003e\u003c/mrow\u003e\u003c/math\u003e\u003c/div\u003e\u003cdiv style=\"text-align:left;margin-bottom:12px;\"\u003e\u003cp\u003e\u003cspan\u003eAsal çarpanlarına ayıralım:\u003c/span\u003e\u003c/p\u003e\u003cmath xmlns=\"http://www.w3.org/1998/Math/MathML\" display=\"block\"\u003e\u003cmrow\u003e\u003cmn\u003e24\u003c/mn\u003e\u003cmo\u003e=\u003c/mo\u003e\u003cmsup\u003e\u003cmn\u003e2\u003c/mn\u003e\u003cmn\u003e3\u003c/mn\u003e\u003c/msup\u003e\u003cmo\u003e·"]) self.__next_f.push([1,"\u003c/mo\u003e\u003cmn\u003e3\u003c/mn\u003e\u003c/mrow\u003e\u003c/math\u003e\u003cmath xmlns=\"http://www.w3.org/1998/Math/MathML\" display=\"block\"\u003e\u003cmrow\u003e\u003cmn\u003e36\u003c/mn\u003e\u003cmo\u003e=\u003c/mo\u003e\u003cmsup\u003e\u003cmn\u003e2\u003c/mn\u003e\u003cmn\u003e2\u003c/mn\u003e\u003c/msup\u003e\u003cmo\u003e·\u003c/mo\u003e\u003cmsup\u003e\u003cmn\u003e3\u003c/mn\u003e\u003cmn\u003e2\u003c/mn\u003e\u003c/msup\u003e\u003c/mrow\u003e\u003c/math\u003e\u003c/div\u003e\u003cdiv style=\"text-align:left;margin-bottom:12px;\"\u003e\u003cp\u003eEKOK alınırken her asal çarpanın kuvveti, iki sayıdaki en büyük kuvvet olarak seçilir:\u003c/p\u003e\u003cmath xmlns=\"http://www.w3.org/1998/Math/MathML\" display=\"block\"\u003e\u003cmrow\u003e\u003cmtext\u003eEKOK\u003c/mtext\u003e\u003cmo\u003e(\u003c/mo\u003e\u003cmn\u003e24\u003c/mn\u003e\u003cmo\u003e,\u003c/mo\u003e\u003cmn\u003e36\u003c/mn\u003e\u003cmo\u003e)\u003c/mo\u003e\u003cmo\u003e=\u003c/mo\u003e\u003cmsup\u003e\u003cmn\u003e2\u003c/mn\u003e\u003cmn\u003e3\u003c/mn\u003e\u003c/msup\u003e\u003cmo\u003e·\u003c/mo\u003e\u003cmsup\u003e\u003cmn\u003e3\u003c/mn\u003e\u003cmn\u003e2\u003c/mn\u003e\u003c/msup\u003e\u003c/mrow\u003e\u003c/math\u003e\u003c/div\u003e\u003cdiv style=\"text-align:left;margin-bottom:12px;\"\u003e\u003cp\u003eÇarpımı hesaplayalım:\u003c/p\u003e\u003cmath xmlns=\"http://www.w3.org/1998/Math/MathML\" display=\"block\"\u003e\u003cmrow\u003e\u003cmsup\u003e\u003cmn\u003e2\u003c/mn\u003e\u003cmn\u003e3\u003c/mn\u003e\u003c/msup\u003e\u003cmo\u003e·\u003c/mo\u003e\u003cmsup\u003e\u003cmn\u003e3\u003c/mn\u003e\u003cmn\u003e2\u003c/mn\u003e\u003c/msup\u003e\u003cmo\u003e=\u003c/mo\u003e\u003cmn\u003e8\u003c/mn\u003e\u003cmo\u003e·\u003c/mo\u003e\u003cmn\u003e9\u003c/mn\u003e\u003cmo\u003e=\u003c/mo\u003e\u003cmn\u003e72\u003c/mn\u003e\u003c/mrow\u003e\u003c/math\u003e\u003c/div\u003e\u003cdiv style=\"text-align:left;margin-bottom:12px;\"\u003e\u003cp\u003eBuna göre doğru cevap \u003cb\u003eC\u003c/b\u003e şıkkıdır.\u003c/p\u003e\u003cmath xmlns=\"http://www.w3.org/1998/Math/MathML\" display=\"block\"\u003e\u003cmrow\u003e\u003cmtext\u003eEKOK\u003c/mtext\u003e\u003cmo\u003e(\u003c/mo\u003e\u003cmn\u003e24\u003c/mn\u003e\u003cmo\u003e,\u003c/mo\u003e\u003cmn\u003e36\u003c/mn\u003e\u003cmo\u003e)\u003c/mo\u003e\u003cmo\u003e=\u003c/mo\u003e\u003cmn\u003e72\u003c/mn\u003e\u003c/mrow\u003e\u003c/math\u003e\u003c/div\u003e21:Tfb8,"]) self.__next_f.push([1,"\u003cdiv style=\"text-align:left;\"\u003e\u003cp style=\"margin:0 0 12px 0;\"\u003eVerilenler:\u003c/p\u003e\u003cdiv style=\"margin:0 0 12px 0;\"\u003e\u003cmath display=\"block\"\u003e\u003cmrow\u003e\u003cmi\u003eEBOB\u003c/mi\u003e\u003cmfenced\u003e\u003cmi\u003ea\u003c/mi\u003e\u003cmo\u003e,\u003c/mo\u003e\u003cmi\u003eb\u003c/mi\u003e\u003c/mfenced\u003e\u003cmo\u003e=\u003c/mo\u003e\u003cmn\u003e24\u003c/mn\u003e\u003c/mrow\u003e\u003c/math\u003e\u003cmath display=\"block\"\u003e\u003cmrow\u003e\u003cmi\u003eEKOK\u003c/mi\u003e\u003cmfenced\u003e\u003cmi\u003ea\u003c/mi\u003e\u003cmo\u003e,\u003c/mo\u003e\u003cmi\u003eb\u003c/mi\u003e\u003c/mfenced\u003e\u003cmo\u003e=\u003c/mo\u003e\u003cmn\u003e1680\u003c/mn\u003e\u003c/mrow\u003e\u003c/math\u003e\u003cmath display=\"block\"\u003e\u003cmrow\u003e\u003cmi\u003ea\u003c/mi\u003e\u003cmo\u003e\u0026lt;\u003c/mo\u003e\u003cmi\u003eb\u003c/mi\u003e\u003c/mrow\u003e\u003c/math\u003e\u003cmath display=\"block\"\u003e\u003cmrow\u003e\u003cmn\u003e7\u003c/mn\u003e\u003cmo\u003e\u0026#x2223;\u003c/mo\u003e\u003cmi\u003ea\u003c/mi\u003e\u003c/mrow\u003e\u003c/math\u003e\u003c/div\u003e\u003cp style=\"margin:0 0 12px 0;\"\u003e1) EBOB–EKOK bağıntısını kullanalım:\u003c/p\u003e\u003cdiv style=\"margin:0 0 12px 0;\"\u003e\u003cmath display=\"block\"\u003e\u003cmrow\u003e\u003cmi\u003ea\u003c/mi\u003e\u003cmo\u003e\u0026#x22C5;\u003c/mo\u003e\u003cmi\u003eb\u003c/mi\u003e\u003cmo\u003e=\u003c/mo\u003e\u003cmi\u003eEBOB\u003c/mi\u003e\u003cmfenced\u003e\u003cmi\u003ea\u003c/mi\u003e\u003cmo\u003e,\u003c/mo\u003e\u003cmi\u003eb\u003c/mi\u003e\u003c/mfenced\u003e\u003cmo\u003e\u0026#x22C5;\u003c/mo\u003e\u003cmi\u003eEKOK\u003c/mi\u003e\u003cmfenced\u003e\u003cmi\u003ea\u003c/mi\u003e\u003cmo\u003e,\u003c/mo\u003e\u003cmi\u003eb\u003c/mi\u003e\u003c/mfenced\u003e\u003c/mrow\u003e\u003c/math\u003e\u003cmath display=\"block\"\u003e\u003cmrow\u003e\u003cmi\u003ea\u003c/mi\u003e\u003cmo\u003e\u0026#x22C5;\u003c/mo\u003e\u003cmi\u003eb\u003c/mi\u003e\u003cmo\u003e=\u003c/mo\u003e\u003cmn\u003e24\u003c/mn\u003e\u003cmo\u003e\u0026#x22C5;\u003c/mo\u003e\u003cmn\u003e1680\u003c/mn\u003e\u003cmo\u003e=\u003c/mo\u003e\u003cmn\u003e40320\u003c/mn\u003e\u003c/mrow\u003e\u003c/math\u003e\u003c/div\u003e\u003cp style=\"margin:0 0 12px 0;\"\u003e2) EBOB 24 olduğuna göre sayıları 24 ile çarpım şeklinde yazalım:\u003c/p\u003e\u003cdiv style=\"margin:0 0 12px 0;\"\u003e\u003cmath display=\"block\"\u003e\u003cmrow\u003e\u003cmi\u003ea\u003c/mi\u003e\u003cmo\u003e=\u003c/mo\u003e\u003cmn\u003e24\u003c/mn\u003e\u003cmi\u003ex\u003c/mi\u003e\u003c/mrow\u003e\u003c/math\u003e\u003cmath display=\"block\"\u003e\u003cmrow\u003e\u003cmi\u003eb\u003c/mi\u003e\u003cmo\u003e=\u003c/mo\u003e\u003cmn\u003e24\u003c/mn\u003e\u003cmi\u003ey\u003c/mi\u003e\u003c/mrow\u003e\u003c/math\u003e\u003cmath display=\"block\"\u003e\u003cmrow\u003e\u003cmi\u003eEBOB\u003c/mi\u003e\u003cmfenced\u003e\u003cmi\u003ex\u003c/mi\u003e\u003cmo\u003e,\u003c/mo\u003e\u003cmi\u003ey\u003c/mi\u003e\u003c/mfenced\u003e\u003cmo\u003e=\u003c/mo\u003e\u003cmn\u003e1\u003c/mn\u003e\u003c/mrow\u003e\u003c/math\u003e\u003c/div\u003e\u003cp style=\"margin:0 0 12px 0;\"\u003e3) EKOK bilgisini kullanalım. EBOB(x,y)=1 iken EKOK(x,y)=x·y olur:\u003c/p\u003e\u003cdiv style=\"margin:0 0 12px 0;\"\u003e\u003cmath display=\"block\"\u003e\u003cmrow\u003e\u003cmi\u003eEKOK\u003c/mi\u003e\u003cmfenced\u003e\u003cmi\u003ea\u003c/mi\u003e\u003cmo\u003e,\u003c/mo\u003e\u003cmi\u003eb\u003c/mi\u003e\u003c/mfenced\u003e\u003cmo\u003e=\u003c/mo\u003e\u003cmn\u003e24\u003c/mn\u003e\u003cmo\u003e\u0026#x22C5;\u003c/mo\u003e\u003cmi\u003ex\u003c/mi\u003e\u003cmo\u003e\u0026#x22C5;\u003c/mo\u003e\u003cmi\u003ey\u003c/mi\u003e\u003c/mrow\u003e\u003c/math\u003e\u003cmath display=\"block\"\u003e\u003cmrow\u003e\u003cmn\u003e1680\u003c/mn\u003e\u003cmo\u003e=\u003c/mo\u003e\u003cmn\u003e24\u003c/mn\u003e\u003cmi\u003ex\u003c/mi\u003e\u003cmi\u003ey\u003c/mi\u003e\u003c/mrow\u003e\u003c/math\u003e\u003cmath display=\"block\"\u003e\u003cmrow\u003e\u003cmi\u003ex\u003c/mi\u003e\u003cmi\u003ey\u003c/mi\u003e\u003cmo\u003e=\u003c/mo\u003e\u003cmfrac\u003e\u003cmn\u003e1680\u003c/mn\u003e\u003cmn\u003e24\u003c/mn\u003e\u003c/mfrac\u003e\u003cmo\u003e=\u003c/mo\u003e\u003cmn\u003e70\u003c/mn\u003e\u003c/mrow\u003e\u003c/math\u003e\u003c/div\u003e\u003cp style=\"margin:0 0 12px 0;\"\u003e4) 7 | a koşulunu x üzerinden yazalım:\u003c/p\u003e\u003cdiv style=\"margin:0 0 12px 0;\"\u003e\u003cmath display=\"block\"\u003e\u003cmrow\u003e\u003cmn\u003e7\u003c/mn\u003e\u003cmo\u003e\u0026#x2223;\u003c/mo\u003e\u003cmi\u003ea\u003c/mi\u003e\u003cmo\u003e=\u003c/mo\u003e\u003cmn\u003e24\u003c/mn\u003e\u003cmi\u003ex\u003c/mi\u003e\u003c/mrow\u003e\u003c/math\u003e\u003cmath display=\"block\"\u003e\u003cmrow\u003e\u003cmn\u003e7\u003c/mn\u003e\u003cmo\u003e\u0026#x2223;\u003c/mo\u003e\u003cmi\u003ex\u003c/mi\u003e\u003c/mrow\u003e\u003c/math\u003e\u003c/div\u003e\u003cp style=\"margin:0 0 12px 0;\"\u003e5) x·y=70 ve EBOB(x,y)=1 olduğundan, 70’in asal çarpanlarını paylaştırırken ortak asal çarpan olmamalı:\u003c/p\u003e\u003cdiv style=\"margin:0 0 12px 0;\"\u003e\u003cmath display=\"block\"\u003e\u003cmrow\u003e\u003cmn\u003e70\u003c/mn\u003e\u003cmo\u003e=\u003c/mo\u003e\u003cmn\u003e2\u003c/mn\u003e\u003cmo\u003e\u0026#x22C5;\u003c/mo\u003e\u003cmn\u003e5\u003c/mn\u003e\u003cmo\u003e\u0026#x22C5;\u003c/mo\u003e\u003cmn\u003e7\u003c/mn\u003e\u003c/mrow\u003e\u003c/math\u003e\u003c/div\u003e\u003cp style=\"margin:0 0 12px 0;\"\u003e6) 7 | x olmalı. Uygun (aralarında asal) çarpan çiftlerini deneyelim:\u003c/p\u003e\u003cdiv style=\"margin:0 0 12px 0;\"\u003e\u003cmath display=\"block\"\u003e\u003cmrow\u003e\u003cmi\u003ex\u003c/mi\u003e\u003cmo\u003e=\u003c/mo\u003e\u003cmn\u003e7\u003c/mn\u003e\u003cmo\u003e\u0026#x21D2;\u003c/mo\u003e\u003cmi\u003ey\u003c/mi\u003e\u003cmo\u003e=\u003c/mo\u003e\u003cmn\u003e10\u003c/mn\u003e\u003cmo\u003e,\u003c/mo\u003e\u003cmi\u003eEBOB\u003c/mi\u003e\u003cmfenced\u003e\u003cmn\u003e7\u003c/mn\u003e\u003cmo\u003e,\u003c/mo\u003e\u003cmn\u003e10\u003c/mn\u003e\u003c/mfenced\u003e\u003cmo\u003e=\u003c/mo\u003e\u003cmn\u003e1\u003c/mn\u003e\u003c/mrow\u003e\u003c/math\u003e\u003cmath display=\"block\"\u003e\u003cmrow\u003e\u003cmi\u003ex\u003c/mi\u003e\u003cmo\u003e=\u003c/mo\u003e\u003cmn\u003e14\u003c/mn\u003e\u003cmo\u003e\u0026#x21D2;\u003c/mo\u003e\u003cmi\u003ey\u003c/mi\u003e\u003cmo\u003e=\u003c/mo\u003e\u003cmn\u003e5\u003c/mn\u003e\u003cmo\u003e,\u003c/mo\u003e\u003cmi\u003eEBOB\u003c/mi\u003e\u003cmfenced\u003e\u003cmn\u003e14\u003c/mn\u003e\u003cmo\u003e,\u003c/mo\u003e\u003cmn\u003e5\u003c/mn\u003e\u003c/mfenced\u003e\u003cmo\u003e=\u003c/mo\u003e\u003cmn\u003e1\u003c/mn\u003e\u003c/mrow\u003e\u003c/math\u003e\u003c/div\u003e\u003cp style=\"margin:0 0 12px 0;\"\u003e7) a\u0026lt;b şartını kontrol edelim. a=24x ve b=24y olduğundan x\u0026lt;y olmalı:\u003c/p\u003e\u003cdiv style=\"margin:0 0 12px 0;\"\u003e\u003cmath display=\"block\"\u003e\u003cmrow\u003e\u003cmi\u003ex\u003c/mi\u003e\u003cmo\u003e=\u003c/mo\u003e\u003cmn\u003e7\u003c/mn\u003e\u003cmo\u003e\u0026lt;\u003c/mo\u003e\u003cmn\u003e10\u003c/mn\u003e\u003cmo\u003e=\u003c/mo\u003e\u003cmi\u003ey\u003c/mi\u003e\u003cmo\u003e\u0026#x2713;\u003c/mo\u003e\u003c/mrow\u003e\u003c/math\u003e\u003cmath display=\"block\"\u003e\u003cmrow\u003e\u003cmi\u003ex\u003c/mi\u003e\u003cmo\u003e=\u003c/mo\u003e\u003cmn\u003e14\u003c/mn\u003e\u003cmo\u003e\u0026gt;\u003c/mo\u003e\u003cmn\u003e5\u003c/mn\u003e\u003cmo\u003e=\u003c/mo\u003e\u003cmi\u003ey\u003c/mi\u003e\u003cmo\u003e\u0026#x2717;\u003c/mo\u003e\u003c/mrow\u003e\u003c/math\u003e\u003c/div\u003e\u003cp style=\"margin:0 0 12px 0;\"\u003e8) O hâlde x=7, y=10:\u003c/p\u003e\u003cdiv style=\"margin:0 0 12px 0;\"\u003e\u003cmath display=\"block\"\u003e\u003cmrow\u003e\u003cmi\u003ea\u003c/mi\u003e\u003cmo\u003e=\u003c/mo\u003e\u003cmn\u003e24\u003c/mn\u003e\u003cmo\u003e\u0026#x22C5;\u003c/mo\u003e\u003cmn\u003e7\u003c/mn\u003e\u003cmo\u003e=\u003c/mo\u003e\u003cmn\u003e168\u003c/mn\u003e\u003c/mrow\u003e\u003c/math\u003e\u003cmath display=\"block\"\u003e\u003cmrow\u003e\u003cmi\u003eb\u003c/mi\u003e\u003cmo\u003e=\u003c/mo\u003e\u003cmn\u003e24\u003c/mn\u003e\u003cmo\u003e\u0026#x22C5;\u003c/mo\u003e\u003cmn\u003e10\u003c/mn\u003e\u003cmo\u003e=\u003c/mo\u003e\u003cmn\u003e240\u003c/mn\u003e\u003c/mrow\u003e\u003c/math\u003e\u003c/div\u003e\u003cp style=\"margin:0 0 0 0;\"\u003eSonuç: Doğru cevap \u003cb\u003eB\u003c/b\u003e şıkkıdır.\u003c/p\u003e\u003c/div\u003e"]) self.__next_f.push([1,"22:T641,\u003cp style=\"text-align:left; margin-bottom:14px;\"\u003eVerilenlere göre iki sayı \u003cmath display=\"block\"\u003e\u003cmi\u003ea\u003c/mi\u003e\u003c/math\u003e ve \u003cmath display=\"block\"\u003e\u003cmi\u003eb\u003c/mi\u003e\u003c/math\u003e olsun.\u003c/p\u003e\u003cp style=\"text-align:left; margin-bottom:14px;\"\u003eBilinen bağıntı:\u003c/p\u003e\u003cdiv style=\"text-align:left; margin-bottom:14px;\"\u003e\u003cmath display=\"block\"\u003e\u003cmi\u003ea\u003c/mi\u003e\u003cmo\u003e\u0026#x00D7;\u003c/mo\u003e\u003cmi\u003eb\u003c/mi\u003e\u003cmo\u003e=\u003c/mo\u003e\u003cmi\u003eEBOB\u003c/mi\u003e\u003cmo\u003e\u0026#x00D7;\u003c/mo\u003e\u003cmi\u003eEKOK\u003c/mi\u003e\u003c/math\u003e\u003c/div\u003e\u003cp style=\"text-align:left; margin-bottom:14px;\"\u003eDeğerleri yerine yazalım:\u003c/p\u003e\u003cdiv style=\"text-align:left; margin-bottom:14px;\"\u003e\u003cmath display=\"block\"\u003e\u003cmi\u003ea\u003c/mi\u003e\u003cmo\u003e\u0026#x00D7;\u003c/mo\u003e\u003cmi\u003eb\u003c/mi\u003e\u003cmo\u003e=\u003c/mo\u003e\u003cmn\u003e12\u003c/mn\u003e\u003cmo\u003e\u0026#x00D7;\u003c/mo\u003e\u003cmn\u003e180\u003c/mn\u003e\u003c/math\u003e\u003c/div\u003e\u003cp style=\"text-align:left; margin-bottom:14px;\"\u003eÇarpımı hesaplayalım:\u003c/p\u003e\u003cdiv style=\"text-align:left; margin-bottom:14px;\"\u003e\u003cmath display=\"block\"\u003e\u003cmi\u003ea\u003c/mi\u003e\u003cmo\u003e\u0026#x00D7;\u003c/mo\u003e\u003cmi\u003eb\u003c/mi\u003e\u003cmo\u003e=\u003c/mo\u003e\u003cmn\u003e2160\u003c/mn\u003e\u003c/math\u003e\u003c/div\u003e\u003cp style=\"text-align:left; margin-bottom:14px;\"\u003eSayıların birinin \u003cmath display=\"block\"\u003e\u003cmn\u003e60\u003c/mn\u003e\u003c/math\u003e olduğu verilmiş. O hâlde:\u003c/p\u003e\u003cdiv style=\"text-align:left; margin-bottom:14px;\"\u003e\u003cmath display=\"block\"\u003e\u003cmn\u003e60\u003c/mn\u003e\u003cmo\u003e\u0026#x00D7;\u003c/mo\u003e\u003cmi\u003ex\u003c/mi\u003e\u003cmo\u003e=\u003c/mo\u003e\u003cmn\u003e2160\u003c/mn\u003e\u003c/math\u003e\u003c/div\u003e\u003cp style=\"text-align:left; margin-bottom:14px;\"\u003eDiğer sayıyı bulmak için bölelim:\u003c/p\u003e\u003cdiv style=\"text-align:left; margin-bottom:14px;\"\u003e\u003cmath display=\"block\"\u003e\u003cmi\u003ex\u003c/mi\u003e\u003cmo\u003e=\u003c/mo\u003e\u003cmfrac\u003e\u003cmn\u003e2160\u003c/mn\u003e\u003cmn\u003e60\u003c/mn\u003e\u003c/mfrac\u003e\u003cmo\u003e=\u003c/mo\u003e\u003cmn\u003e36\u003c/mn\u003e\u003c/math\u003e\u003c/div\u003e\u003cp style=\"text-align:left; margin-bottom:14px;\"\u003eBulunan değer \u003cmath display=\"block\"\u003e\u003cmn\u003e36\u003c/mn\u003e\u003c/math\u003e olduğundan doğru seçenek \u003cb\u003eC\u003c/b\u003e'dir; yani \u003cb\u003eC doğru\u003c/b\u003e.\u003c/p\u003e23:Te00,"]) self.__next_f.push([1,"\u003cdiv style=\"text-align:left;margin-bottom:14px;\"\u003e\u003cp style=\"margin:0 0 10px 0;\"\u003eVerilenler:\u003c/p\u003e\u003cmath display=\"block\"\u003e\u003cmrow\u003e\u003cmi\u003eEBOB\u003c/mi\u003e\u003cmo\u003e(\u003c/mo\u003e\u003cmi\u003ea\u003c/mi\u003e\u003cmo\u003e,\u003c/mo\u003e\u003cmi\u003eb\u003c/mi\u003e\u003cmo\u003e)\u003c/mo\u003e\u003cmo\u003e=\u003c/mo\u003e\u003cmn\u003e18\u003c/mn\u003e\u003c/mrow\u003e\u003c/math\u003e\u003cmath display=\"block\"\u003e\u003cmrow\u003e\u003cmi\u003eEKOK\u003c/mi\u003e\u003cmo\u003e(\u003c/mo\u003e\u003cmi\u003ea\u003c/mi\u003e\u003cmo\u003e,\u003c/mo\u003e\u003cmi\u003eb\u003c/mi\u003e\u003cmo\u003e)\u003c/mo\u003e\u003cmo\u003e=\u003c/mo\u003e\u003cmn\u003e1260\u003c/mn\u003e\u003c/mrow\u003e\u003c/math\u003e\u003c/div\u003e\u003cdiv style=\"text-align:left;margin-bottom:14px;\"\u003e\u003cp style=\"margin:0 0 10px 0;\"\u003eBilinen bağıntı:\u003c/p\u003e\u003cmath display=\"block\"\u003e\u003cmrow\u003e\u003cmi\u003ea\u003c/mi\u003e\u003cmo\u003e⋅\u003c/mo\u003e\u003cmi\u003eb\u003c/mi\u003e\u003cmo\u003e=\u003c/mo\u003e\u003cmi\u003eEBOB\u003c/mi\u003e\u003cmo\u003e(\u003c/mo\u003e\u003cmi\u003ea\u003c/mi\u003e\u003cmo\u003e,\u003c/mo\u003e\u003cmi\u003eb\u003c/mi\u003e\u003cmo\u003e)\u003c/mo\u003e\u003cmo\u003e⋅\u003c/mo\u003e\u003cmi\u003eEKOK\u003c/mi\u003e\u003cmo\u003e(\u003c/mo\u003e\u003cmi\u003ea\u003c/mi\u003e\u003cmo\u003e,\u003c/mo\u003e\u003cmi\u003eb\u003c/mi\u003e\u003cmo\u003e)\u003c/mo\u003e\u003c/mrow\u003e\u003c/math\u003e\u003cp style=\"margin:0 0 10px 0;\"\u003eBuradan:\u003c/p\u003e\u003cmath display=\"block\"\u003e\u003cmrow\u003e\u003cmi\u003ea\u003c/mi\u003e\u003cmo\u003e⋅\u003c/mo\u003e\u003cmi\u003eb\u003c/mi\u003e\u003cmo\u003e=\u003c/mo\u003e\u003cmn\u003e18\u003c/mn\u003e\u003cmo\u003e⋅\u003c/mo\u003e\u003cmn\u003e1260\u003c/mn\u003e\u003cmo\u003e=\u003c/mo\u003e\u003cmn\u003e22680\u003c/mn\u003e\u003c/mrow\u003e\u003c/math\u003e\u003c/div\u003e\u003cdiv style=\"text-align:left;margin-bottom:14px;\"\u003e\u003cp style=\"margin:0 0 10px 0;\"\u003eOrtak böleni ayıralım:\u003c/p\u003e\u003cmath display=\"block\"\u003e\u003cmrow\u003e\u003cmi\u003ea\u003c/mi\u003e\u003cmo\u003e=\u003c/mo\u003e\u003cmn\u003e18\u003c/mn\u003e\u003cmi\u003ex\u003c/mi\u003e\u003c/mrow\u003e\u003c/math\u003e\u003cmath display=\"block\"\u003e\u003cmrow\u003e\u003cmi\u003eb\u003c/mi\u003e\u003cmo\u003e=\u003c/mo\u003e\u003cmn\u003e18\u003c/mn\u003e\u003cmi\u003ey\u003c/mi\u003e\u003c/mrow\u003e\u003c/math\u003e\u003cp style=\"margin:0 0 10px 0;\"\u003eBu durumda:\u003c/p\u003e\u003cmath display=\"block\"\u003e\u003cmrow\u003e\u003cmi\u003eEBOB\u003c/mi\u003e\u003cmo\u003e(\u003c/mo\u003e\u003cmi\u003ex\u003c/mi\u003e\u003cmo\u003e,\u003c/mo\u003e\u003cmi\u003ey\u003c/mi\u003e\u003cmo\u003e)\u003c/mo\u003e\u003cmo\u003e=\u003c/mo\u003e\u003cmn\u003e1\u003c/mn\u003e\u003c/mrow\u003e\u003c/math\u003e\u003c/div\u003e\u003cdiv style=\"text-align:left;margin-bottom:14px;\"\u003e\u003cp style=\"margin:0 0 10px 0;\"\u003eEKOK bağıntısını kullanalım:\u003c/p\u003e\u003cmath display=\"block\"\u003e\u003cmrow\u003e\u003cmi\u003eEKOK\u003c/mi\u003e\u003cmo\u003e(\u003c/mo\u003e\u003cmi\u003ea\u003c/mi\u003e\u003cmo\u003e,\u003c/mo\u003e\u003cmi\u003eb\u003c/mi\u003e\u003cmo\u003e)\u003c/mo\u003e\u003cmo\u003e=\u003c/mo\u003e\u003cmn\u003e18\u003c/mn\u003e\u003cmi\u003ex\u003c/mi\u003e\u003cmi\u003ey\u003c/mi\u003e\u003c/mrow\u003e\u003c/math\u003e\u003cp style=\"margin:0 0 10px 0;\"\u003eVerilen EKOK değerini yazınca:\u003c/p\u003e\u003cmath display=\"block\"\u003e\u003cmrow\u003e\u003cmn\u003e18\u003c/mn\u003e\u003cmi\u003ex\u003c/mi\u003e\u003cmi\u003ey\u003c/mi\u003e\u003cmo\u003e=\u003c/mo\u003e\u003cmn\u003e1260\u003c/mn\u003e\u003c/mrow\u003e\u003c/math\u003e\u003cmath display=\"block\"\u003e\u003cmrow\u003e\u003cmi\u003ex\u003c/mi\u003e\u003cmi\u003ey\u003c/mi\u003e\u003cmo\u003e=\u003c/mo\u003e\u003cmn\u003e70\u003c/mn\u003e\u003c/mrow\u003e\u003c/math\u003e\u003c/div\u003e\u003cdiv style=\"text-align:left;margin-bottom:14px;\"\u003e\u003cp style=\"margin:0 0 10px 0;\"\u003eŞimdi \u003cmath display=\"block\"\u003e\u003cmrow\u003e\u003cmi\u003eEBOB\u003c/mi\u003e\u003cmo\u003e(\u003c/mo\u003e\u003cmi\u003ex\u003c/mi\u003e\u003cmo\u003e,\u003c/mo\u003e\u003cmi\u003ey\u003c/mi\u003e\u003cmo\u003e)\u003c/mo\u003e\u003cmo\u003e=\u003c/mo\u003e\u003cmn\u003e1\u003c/mn\u003e\u003c/mrow\u003e\u003c/math\u003e şartıyla \u003cmath display=\"block\"\u003e\u003cmrow\u003e\u003cmi\u003ex\u003c/mi\u003e\u003cmi\u003ey\u003c/mi\u003e\u003cmo\u003e=\u003c/mo\u003e\u003cmn\u003e70\u003c/mn\u003e\u003c/mrow\u003e\u003c/math\u003e çarpan çiftlerini yazalım (aralarında asal olanlar):\u003c/p\u003e\u003cmath display=\"block\"\u003e\u003cmrow\u003e\u003cmo\u003e(\u003c/mo\u003e\u003cmn\u003e1\u003c/mn\u003e\u003cmo\u003e,\u003c/mo\u003e\u003cmn\u003e70\u003c/mn\u003e\u003cmo\u003e)\u003c/mo\u003e\u003c/mrow\u003e\u003c/math\u003e\u003cmath display=\"block\"\u003e\u003cmrow\u003e\u003cmo\u003e(\u003c/mo\u003e\u003cmn\u003e2\u003c/mn\u003e\u003cmo\u003e,\u003c/mo\u003e\u003cmn\u003e35\u003c/mn\u003e\u003cmo\u003e)\u003c/mo\u003e\u003c/mrow\u003e\u003c/math\u003e\u003cmath display=\"block\"\u003e\u003cmrow\u003e\u003cmo\u003e(\u003c/mo\u003e\u003cmn\u003e5\u003c/mn\u003e\u003cmo\u003e,\u003c/mo\u003e\u003cmn\u003e14\u003c/mn\u003e\u003cmo\u003e)\u003c/mo\u003e\u003c/mrow\u003e\u003c/math\u003e\u003cmath display=\"block\"\u003e\u003cmrow\u003e\u003cmo\u003e(\u003c/mo\u003e\u003cmn\u003e7\u003c/mn\u003e\u003cmo\u003e,\u003c/mo\u003e\u003cmn\u003e10\u003c/mn\u003e\u003cmo\u003e)\u003c/mo\u003e\u003c/mrow\u003e\u003c/math\u003e\u003c/div\u003e\u003cdiv style=\"text-align:left;margin-bottom:14px;\"\u003e\u003cp style=\"margin:0 0 10px 0;\"\u003eToplam:\u003c/p\u003e\u003cmath display=\"block\"\u003e\u003cmrow\u003e\u003cmi\u003ea\u003c/mi\u003e\u003cmo\u003e+\u003c/mo\u003e\u003cmi\u003eb\u003c/mi\u003e\u003cmo\u003e=\u003c/mo\u003e\u003cmn\u003e18\u003c/mn\u003e\u003cmi\u003ex\u003c/mi\u003e\u003cmo\u003e+\u003c/mo\u003e\u003cmn\u003e18\u003c/mn\u003e\u003cmi\u003ey\u003c/mi\u003e\u003cmo\u003e=\u003c/mo\u003e\u003cmn\u003e18\u003c/mn\u003e\u003cmo\u003e(\u003c/mo\u003e\u003cmi\u003ex\u003c/mi\u003e\u003cmo\u003e+\u003c/mo\u003e\u003cmi\u003ey\u003c/mi\u003e\u003cmo\u003e)\u003c/mo\u003e\u003c/mrow\u003e\u003c/math\u003e\u003cp style=\"margin:0 0 10px 0;\"\u003eEn küçük toplam için \u003cmath display=\"block\"\u003e\u003cmrow\u003e\u003cmi\u003ex\u003c/mi\u003e\u003cmo\u003e+\u003c/mo\u003e\u003cmi\u003ey\u003c/mi\u003e\u003c/mrow\u003e\u003c/math\u003e en küçük olmalı. Yukarıdaki çiftlerde en küçük toplam:\u003c/p\u003e\u003cmath display=\"block\"\u003e\u003cmrow\u003e\u003cmn\u003e7\u003c/mn\u003e\u003cmo\u003e+\u003c/mo\u003e\u003cmn\u003e10\u003c/mn\u003e\u003cmo\u003e=\u003c/mo\u003e\u003cmn\u003e17\u003c/mn\u003e\u003c/mrow\u003e\u003c/math\u003e\u003cp style=\"margin:0 0 10px 0;\"\u003eDolayısıyla:\u003c/p\u003e\u003cmath display=\"block\"\u003e\u003cmrow\u003e\u003cmi\u003ea\u003c/mi\u003e\u003cmo\u003e+\u003c/mo\u003e\u003cmi\u003eb\u003c/mi\u003e\u003cmo\u003e=\u003c/mo\u003e\u003cmn\u003e18\u003c/mn\u003e\u003cmo\u003e⋅\u003c/mo\u003e\u003cmn\u003e17\u003c/mn\u003e\u003cmo\u003e=\u003c/mo\u003e\u003cmn\u003e306\u003c/mn\u003e\u003c/mrow\u003e\u003c/math\u003e\u003c/div\u003e\u003cdiv style=\"text-align:left;margin-bottom:0px;\"\u003e\u003cp style=\"margin:0 0 10px 0;\"\u003eSonuç: En küçük değer \u003cmath display=\"block\"\u003e\u003cmrow\u003e\u003cmn\u003e306\u003c/mn\u003e\u003c/mrow\u003e\u003c/math\u003e olur. Bu da \u003cstrong\u003eB\u003c/strong\u003e şıkkıdır; yani B doğru.\u003c/p\u003e\u003c/div\u003e"]) self.__next_f.push([1,"24:T6a9,\u003cdiv style=\"text-align:left;\"\u003e\u003cp style=\"margin:0 0 12px 0;\"\u003eİşlem:\u003c/p\u003e\u003cmath display=\"block\"\u003e\u003cmrow\u003e\u003cmi\u003eEBOB\u003c/mi\u003e\u003cmo\u003e(\u003c/mo\u003e\u003cmn\u003e36\u003c/mn\u003e\u003cmo\u003e,\u003c/mo\u003e\u003cmn\u003e48\u003c/mn\u003e\u003cmo\u003e)\u003c/mo\u003e\u003cmo\u003e+\u003c/mo\u003e\u003cmi\u003eEKOK\u003c/mi\u003e\u003cmo\u003e(\u003c/mo\u003e\u003cmn\u003e36\u003c/mn\u003e\u003cmo\u003e,\u003c/mo\u003e\u003cmn\u003e48\u003c/mn\u003e\u003cmo\u003e)\u003c/mo\u003e\u003c/mrow\u003e\u003c/math\u003e\u003cp style=\"margin:0 0 12px 0;\"\u003eÖnce sayıları asal çarpanlarına ayıralım:\u003c/p\u003e\u003cmath display=\"block\"\u003e\u003cmrow\u003e\u003cmn\u003e36\u003c/mn\u003e\u003cmo\u003e=\u003c/mo\u003e\u003cmsup\u003e\u003cmn\u003e2\u003c/mn\u003e\u003cmn\u003e2\u003c/mn\u003e\u003c/msup\u003e\u003cmo\u003e·\u003c/mo\u003e\u003cmsup\u003e\u003cmn\u003e3\u003c/mn\u003e\u003cmn\u003e2\u003c/mn\u003e\u003c/msup\u003e\u003c/mrow\u003e\u003c/math\u003e\u003cmath display=\"block\"\u003e\u003cmrow\u003e\u003cmn\u003e48\u003c/mn\u003e\u003cmo\u003e=\u003c/mo\u003e\u003cmsup\u003e\u003cmn\u003e2\u003c/mn\u003e\u003cmn\u003e4\u003c/mn\u003e\u003c/msup\u003e\u003cmo\u003e·\u003c/mo\u003e\u003cmn\u003e3\u003c/mn\u003e\u003c/mrow\u003e\u003c/math\u003e\u003cp style=\"margin:0 0 12px 0;\"\u003eEBOB, ortak asal çarpanların üslerinin küçük olanları alınarak bulunur:\u003c/p\u003e\u003cmath display=\"block\"\u003e\u003cmrow\u003e\u003cmi\u003eEBOB\u003c/mi\u003e\u003cmo\u003e(\u003c/mo\u003e\u003cmn\u003e36\u003c/mn\u003e\u003cmo\u003e,\u003c/mo\u003e\u003cmn\u003e48\u003c/mn\u003e\u003cmo\u003e)\u003c/mo\u003e\u003cmo\u003e=\u003c/mo\u003e\u003cmsup\u003e\u003cmn\u003e2\u003c/mn\u003e\u003cmn\u003e2\u003c/mn\u003e\u003c/msup\u003e\u003cmo\u003e·\u003c/mo\u003e\u003cmn\u003e3\u003c/mn\u003e\u003cmo\u003e=\u003c/mo\u003e\u003cmn\u003e12\u003c/mn\u003e\u003c/mrow\u003e\u003c/math\u003e\u003cp style=\"margin:0 0 12px 0;\"\u003eEKOK, asal çarpanların üslerinin büyük olanları alınarak bulunur:\u003c/p\u003e\u003cmath display=\"block\"\u003e\u003cmrow\u003e\u003cmi\u003eEKOK\u003c/mi\u003e\u003cmo\u003e(\u003c/mo\u003e\u003cmn\u003e36\u003c/mn\u003e\u003cmo\u003e,\u003c/mo\u003e\u003cmn\u003e48\u003c/mn\u003e\u003cmo\u003e)\u003c/mo\u003e\u003cmo\u003e=\u003c/mo\u003e\u003cmsup\u003e\u003cmn\u003e2\u003c/mn\u003e\u003cmn\u003e4\u003c/mn\u003e\u003c/msup\u003e\u003cmo\u003e·\u003c/mo\u003e\u003cmsup\u003e\u003cmn\u003e3\u003c/mn\u003e\u003cmn\u003e2\u003c/mn\u003e\u003c/msup\u003e\u003cmo\u003e=\u003c/mo\u003e\u003cmn\u003e16\u003c/mn\u003e\u003cmo\u003e·\u003c/mo\u003e\u003cmn\u003e9\u003c/mn\u003e\u003cmo\u003e=\u003c/mo\u003e\u003cmn\u003e144\u003c/mn\u003e\u003c/mrow\u003e\u003c/math\u003e\u003cp style=\"margin:0 0 12px 0;\"\u003eŞimdi toplamı hesaplayalım:\u003c/p\u003e\u003cmath display=\"block\"\u003e\u003cmrow\u003e\u003cmi\u003eEBOB\u003c/mi\u003e\u003cmo\u003e(\u003c/mo\u003e\u003cmn\u003e36\u003c/mn\u003e\u003cmo\u003e,\u003c/mo\u003e\u003cmn\u003e48\u003c/mn\u003e\u003cmo\u003e)\u003c/mo\u003e\u003cmo\u003e+\u003c/mo\u003e\u003cmi\u003eEKOK\u003c/mi\u003e\u003cmo\u003e(\u003c/mo\u003e\u003cmn\u003e36\u003c/mn\u003e\u003cmo\u003e,\u003c/mo\u003e\u003cmn\u003e48\u003c/mn\u003e\u003cmo\u003e)\u003c/mo\u003e\u003cmo\u003e=\u003c/mo\u003e\u003cmn\u003e12\u003c/mn\u003e\u003cmo\u003e+\u003c/mo\u003e\u003cmn\u003e144\u003c/mn\u003e\u003cmo\u003e=\u003c/mo\u003e\u003cmn\u003e156\u003c/mn\u003e\u003c/mrow\u003e\u003c/math\u003e\u003cp style=\"margin:0 0 12px 0;\"\u003eSonuç \u003cmath display=\"block\"\u003e\u003cmn\u003e156\u003c/mn\u003e\u003c/math\u003e olduğundan doğru seçenek \u003cb\u003eB\u003c/b\u003e’dir.\u003c/p\u003e\u003c/div\u003e25:T11f8,"]) self.__next_f.push([1,"\u003cdiv style=\"text-align:left;\"\u003e\u003cp style=\"margin-bottom:14px; text-align:left;\"\u003eVerilenler:\u003c/p\u003e\u003cdiv style=\"margin-bottom:14px; text-align:left;\"\u003e\u003cmath display=\"block\"\u003e\u003cmrow\u003e\u003cmtext\u003eEBOB\u003c/mtext\u003e\u003cmo\u003e(\u003c/mo\u003e\u003cmi\u003ea\u003c/mi\u003e\u003cmo\u003e,\u003c/mo\u003e\u003cmi\u003eb\u003c/mi\u003e\u003cmo\u003e)\u003c/mo\u003e\u003cmo\u003e=\u003c/mo\u003e\u003cmn\u003e18\u003c/mn\u003e\u003c/mrow\u003e\u003c/math\u003e\u003cmath display=\"block\"\u003e\u003cmrow\u003e\u003cmtext\u003eEKOK\u003c/mtext\u003e\u003cmo\u003e(\u003c/mo\u003e\u003cmi\u003ea\u003c/mi\u003e\u003cmo\u003e,\u003c/mo\u003e\u003cmi\u003eb\u003c/mi\u003e\u003cmo\u003e)\u003c/mo\u003e\u003cmo\u003e=\u003c/mo\u003e\u003cmn\u003e540\u003c/mn\u003e\u003c/mrow\u003e\u003c/math\u003e\u003cmath display=\"block\"\u003e\u003cmrow\u003e\u003cmn\u003e90\u003c/mn\u003e\u003cmo\u003e\u0026#x2223;\u003c/mo\u003e\u003cmi\u003ea\u003c/mi\u003e\u003c/mrow\u003e\u003c/math\u003e\u003cmath display=\"block\"\u003e\u003cmrow\u003e\u003cmi\u003ea\u003c/mi\u003e\u003cmo\u003e\u0026lt;\u003c/mo\u003e\u003cmi\u003eb\u003c/mi\u003e\u003c/mrow\u003e\u003c/math\u003e\u003c/div\u003e\u003cp style=\"margin-bottom:14px; text-align:left;\"\u003e1) EBOB–EKOK bağıntısı:\u003c/p\u003e\u003cdiv style=\"margin-bottom:14px; text-align:left;\"\u003e\u003cmath display=\"block\"\u003e\u003cmrow\u003e\u003cmi\u003ea\u003c/mi\u003e\u003cmo\u003e\u0026#x22C5;\u003c/mo\u003e\u003cmi\u003eb\u003c/mi\u003e\u003cmo\u003e=\u003c/mo\u003e\u003cmtext\u003eEBOB\u003c/mtext\u003e\u003cmo\u003e(\u003c/mo\u003e\u003cmi\u003ea\u003c/mi\u003e\u003cmo\u003e,\u003c/mo\u003e\u003cmi\u003eb\u003c/mi\u003e\u003cmo\u003e)\u003c/mo\u003e\u003cmo\u003e\u0026#x22C5;\u003c/mo\u003e\u003cmtext\u003eEKOK\u003c/mtext\u003e\u003cmo\u003e(\u003c/mo\u003e\u003cmi\u003ea\u003c/mi\u003e\u003cmo\u003e,\u003c/mo\u003e\u003cmi\u003eb\u003c/mi\u003e\u003cmo\u003e)\u003c/mo\u003e\u003c/mrow\u003e\u003c/math\u003e\u003cmath display=\"block\"\u003e\u003cmrow\u003e\u003cmi\u003ea\u003c/mi\u003e\u003cmo\u003e\u0026#x22C5;\u003c/mo\u003e\u003cmi\u003eb\u003c/mi\u003e\u003cmo\u003e=\u003c/mo\u003e\u003cmn\u003e18\u003c/mn\u003e\u003cmo\u003e\u0026#x22C5;\u003c/mo\u003e\u003cmn\u003e540\u003c/mn\u003e\u003cmo\u003e=\u003c/mo\u003e\u003cmn\u003e9720\u003c/mn\u003e\u003c/mrow\u003e\u003c/math\u003e\u003c/div\u003e\u003cp style=\"margin-bottom:14px; text-align:left;\"\u003e2) EBOB ile sadeleştirme:\u003c/p\u003e\u003cdiv style=\"margin-bottom:14px; text-align:left;\"\u003e\u003cmath display=\"block\"\u003e\u003cmrow\u003e\u003cmi\u003ea\u003c/mi\u003e\u003cmo\u003e=\u003c/mo\u003e\u003cmn\u003e18\u003c/mn\u003e\u003cmi\u003ex\u003c/mi\u003e\u003c/mrow\u003e\u003c/math\u003e\u003cmath display=\"block\"\u003e\u003cmrow\u003e\u003cmi\u003eb\u003c/mi\u003e\u003cmo\u003e=\u003c/mo\u003e\u003cmn\u003e18\u003c/mn\u003e\u003cmi\u003ey\u003c/mi\u003e\u003c/mrow\u003e\u003c/math\u003e\u003cmath display=\"block\"\u003e\u003cmrow\u003e\u003cmtext\u003eEBOB\u003c/mtext\u003e\u003cmo\u003e(\u003c/mo\u003e\u003cmi\u003ex\u003c/mi\u003e\u003cmo\u003e,\u003c/mo\u003e\u003cmi\u003ey\u003c/mi\u003e\u003cmo\u003e)\u003c/mo\u003e\u003cmo\u003e=\u003c/mo\u003e\u003cmn\u003e1\u003c/mn\u003e\u003c/mrow\u003e\u003c/math\u003e\u003c/div\u003e\u003cp style=\"margin-bottom:14px; text-align:left;\"\u003e3) EKOK koşulundan çarpım:\u003c/p\u003e\u003cdiv style=\"margin-bottom:14px; text-align:left;\"\u003e\u003cmath display=\"block\"\u003e\u003cmrow\u003e\u003cmtext\u003eEKOK\u003c/mtext\u003e\u003cmo\u003e(\u003c/mo\u003e\u003cmi\u003ea\u003c/mi\u003e\u003cmo\u003e,\u003c/mo\u003e\u003cmi\u003eb\u003c/mi\u003e\u003cmo\u003e)\u003c/mo\u003e\u003cmo\u003e=\u003c/mo\u003e\u003cmn\u003e18\u003c/mn\u003e\u003cmi\u003ex\u003c/mi\u003e\u003cmi\u003ey\u003c/mi\u003e\u003c/mrow\u003e\u003c/math\u003e\u003cmath display=\"block\"\u003e\u003cmrow\u003e\u003cmn\u003e18\u003c/mn\u003e\u003cmi\u003ex\u003c/mi\u003e\u003cmi\u003ey\u003c/mi\u003e\u003cmo\u003e=\u003c/mo\u003e\u003cmn\u003e540\u003c/mn\u003e\u003c/mrow\u003e\u003c/math\u003e\u003cmath display=\"block\"\u003e\u003cmrow\u003e\u003cmi\u003ex\u003c/mi\u003e\u003cmi\u003ey\u003c/mi\u003e\u003cmo\u003e=\u003c/mo\u003e\u003cmn\u003e30\u003c/mn\u003e\u003c/mrow\u003e\u003c/math\u003e\u003c/div\u003e\u003cp style=\"margin-bottom:14px; text-align:left;\"\u003e4) \u003cspan style=\"text-align:left;\"\u003eBölünebilme şartını\u003c/span\u003e\u003cspan style=\"text-align:left;\"\u003ekullanalım:\u003c/span\u003e\u003c/p\u003e\u003cdiv style=\"margin-bottom:14px; text-align:left;\"\u003e\u003cmath display=\"block\"\u003e\u003cmrow\u003e\u003cmn\u003e90\u003c/mn\u003e\u003cmo\u003e\u0026#x2223;\u003c/mo\u003e\u003cmi\u003ea\u003c/mi\u003e\u003c/mrow\u003e\u003c/math\u003e\u003cmath display=\"block\"\u003e\u003cmrow\u003e\u003cmn\u003e90\u003c/mn\u003e\u003cmo\u003e\u0026#x2223;\u003c/mo\u003e\u003cmn\u003e18\u003c/mn\u003e\u003cmi\u003ex\u003c/mi\u003e\u003c/mrow\u003e\u003c/math\u003e\u003cmath display=\"block\"\u003e\u003cmrow\u003e\u003cmn\u003e5\u003c/mn\u003e\u003cmo\u003e\u0026#x2223;\u003c/mo\u003e\u003cmi\u003ex\u003c/mi\u003e\u003c/mrow\u003e\u003c/math\u003e\u003c/div\u003e\u003cp style=\"margin-bottom:14px; text-align:left;\"\u003e5) \u003cspan style=\"text-align:left;\"\u003eŞimdi\u003c/span\u003e\u003cspan style=\"text-align:left;\"\u003ehem\u003c/span\u003e\u003cspan style=\"text-align:left;\"\u003eçarpım\u003c/span\u003e\u003cspan style=\"text-align:left;\"\u003ehem\u003c/span\u003e\u003cspan style=\"text-align:left;\"\u003earalarında\u003c/span\u003e\u003cspan style=\"text-align:left;\"\u003easal\u003c/span\u003e\u003cspan style=\"text-align:left;\"\u003eolma\u003c/span\u003e\u003cspan style=\"text-align:left;\"\u003eşartı:\u003c/span\u003e\u003c/p\u003e\u003cdiv style=\"margin-bottom:14px; text-align:left;\"\u003e\u003cmath display=\"block\"\u003e\u003cmrow\u003e\u003cmi\u003ex\u003c/mi\u003e\u003cmi\u003ey\u003c/mi\u003e\u003cmo\u003e=\u003c/mo\u003e\u003cmn\u003e30\u003c/mn\u003e\u003c/mrow\u003e\u003c/math\u003e\u003cmath display=\"block\"\u003e\u003cmrow\u003e\u003cmtext\u003eEBOB\u003c/mtext\u003e\u003cmo\u003e(\u003c/mo\u003e\u003cmi\u003ex\u003c/mi\u003e\u003cmo\u003e,\u003c/mo\u003e\u003cmi\u003ey\u003c/mi\u003e\u003cmo\u003e)\u003c/mo\u003e\u003cmo\u003e=\u003c/mo\u003e\u003cmn\u003e1\u003c/mn\u003e\u003c/mrow\u003e\u003c/math\u003e\u003cmath display=\"block\"\u003e\u003cmrow\u003e\u003cmn\u003e5\u003c/mn\u003e\u003cmo\u003e\u0026#x2223;\u003c/mo\u003e\u003cmi\u003ex\u003c/mi\u003e\u003c/mrow\u003e\u003c/math\u003e\u003c/div\u003e\u003cp style=\"margin-bottom:14px; text-align:left;\"\u003eBu koşulları sağlayan uygun çarpan çifti:\u003c/p\u003e\u003cdiv style=\"margin-bottom:14px; text-align:left;\"\u003e\u003cmath display=\"block\"\u003e\u003cmrow\u003e\u003cmi\u003ex\u003c/mi\u003e\u003cmo\u003e=\u003c/mo\u003e\u003cmn\u003e5\u003c/mn\u003e\u003cmo\u003e,\u003c/mo\u003e\u003cmi\u003ey\u003c/mi\u003e\u003cmo\u003e=\u003c/mo\u003e\u003cmn\u003e6\u003c/mn\u003e\u003c/mrow\u003e\u003c/math\u003e\u003cmath display=\"block\"\u003e\u003cmrow\u003e\u003cmtext\u003eEBOB\u003c/mtext\u003e\u003cmo\u003e(\u003c/mo\u003e\u003cmn\u003e5\u003c/mn\u003e\u003cmo\u003e,\u003c/mo\u003e\u003cmn\u003e6\u003c/mn\u003e\u003cmo\u003e)\u003c/mo\u003e\u003cmo\u003e=\u003c/mo\u003e\u003cmn\u003e1\u003c/mn\u003e\u003c/mrow\u003e\u003c/math\u003e\u003c/div\u003e\u003cp style=\"margin-bottom:14px; text-align:left;\"\u003e6) \u003cspan style=\"text-align:left;\"\u003eBuna\u003c/span\u003e\u003cspan style=\"text-align:left;\"\u003egöre\u003c/span\u003e\u003cspan style=\"text-align:left;\"\u003esayılara\u003c/span\u003e\u003cspan style=\"text-align:left;\"\u003edönelim\u003c/span\u003e\u003cspan style=\"text-align:left;\"\u003eve\u003c/span\u003e\u003cspan style=\"text-align:left;\"\u003efarkı\u003c/span\u003e\u003cspan style=\"text-align:left;\"\u003ebulalım:\u003c/span\u003e\u003c/p\u003e\u003cdiv style=\"margin-bottom:14px; text-align:left;\"\u003e\u003cmath display=\"block\"\u003e\u003cmrow\u003e\u003cmi\u003ea\u003c/mi\u003e\u003cmo\u003e=\u003c/mo\u003e\u003cmn\u003e18\u003c/mn\u003e\u003cmo\u003e\u0026#x22C5;\u003c/mo\u003e\u003cmn\u003e5\u003c/mn\u003e\u003cmo\u003e=\u003c/mo\u003e\u003cmn\u003e90\u003c/mn\u003e\u003c/mrow\u003e\u003c/math\u003e\u003cmath display=\"block\"\u003e\u003cmrow\u003e\u003cmi\u003eb\u003c/mi\u003e\u003cmo\u003e=\u003c/mo\u003e\u003cmn\u003e18\u003c/mn\u003e\u003cmo\u003e\u0026#x22C5;\u003c/mo\u003e\u003cmn\u003e6\u003c/mn\u003e\u003cmo\u003e=\u003c/mo\u003e\u003cmn\u003e108\u003c/mn\u003e\u003c/mrow\u003e\u003c/math\u003e\u003cmath display=\"block\"\u003e\u003cmrow\u003e\u003cmi\u003ea\u003c/mi\u003e\u003cmo\u003e\u0026lt;\u003c/mo\u003e\u003cmi\u003eb\u003c/mi\u003e\u003c/mrow\u003e\u003c/math\u003e\u003cmath display=\"block\"\u003e\u003cmrow\u003e\u003cmi\u003eb\u003c/mi\u003e\u003cmo\u003e-\u003c/mo\u003e\u003cmi\u003ea\u003c/mi\u003e\u003cmo\u003e=\u003c/mo\u003e\u003cmn\u003e108\u003c/mn\u003e\u003cmo\u003e-\u003c/mo\u003e\u003cmn\u003e90\u003c/mn\u003e\u003cmo\u003e=\u003c/mo\u003e\u003cmn\u003e18\u003c/mn\u003e\u003c/mrow\u003e\u003c/math\u003e\u003c/div\u003e\u003cp style=\"margin-bottom:0px; text-align:left;\"\u003eSonuç: Doğru cevap \u003cb\u003eA\u003c/b\u003e seçeneğidir.\u003c/p\u003e\u003c/div\u003e"]) self.__next_f.push([1,"17:[\"$\",\"main\",null,{\"className\":\"min-h-screen bg-white text-slate-950\",\"children\":[[[\"$\",\"script\",\"international-test-schema-0\",{\"type\":\"application/ld+json\",\"children\":\"$19\"}]],[[\"$\",\"section\",null,{\"className\":\"border-b border-slate-200 bg-[#f7f8fb]\",\"children\":[\"$\",\"div\",null,{\"className\":\"mx-auto grid max-w-6xl gap-6 px-4 py-7 sm:px-6 lg:grid-cols-[minmax(0,1fr)_320px] lg:px-8 lg:py-8\",\"children\":[[\"$\",\"div\",null,{\"className\":\"min-w-0\",\"children\":[[\"$\",\"p\",null,{\"className\":\"text-xs font-bold uppercase tracking-wide text-[#4b4ee6]\",\"children\":\"9. Sınıf Matematik\"}],[\"$\",\"h1\",null,{\"className\":\"mt-3 max-w-3xl font-display text-4xl font-bold leading-tight text-slate-950 sm:text-5xl\",\"children\":\"9. Sınıf Matematik Ebob Ekok Testleri\"}],[\"$\",\"p\",null,{\"className\":\"mt-4 max-w-2xl text-lg leading-7 text-slate-600\",\"children\":\"EBOB-EKOK konusundaki soruları çözümlü testlerle pekiştir.\"}],null]}],null]}]}],[\"$\",\"section\",null,{\"className\":\"mx-auto max-w-4xl px-4 py-5 sm:px-6 lg:px-8\",\"children\":[\"$\",\"div\",null,{\"className\":\"$1a\",\"dangerouslySetInnerHTML\":{\"__html\":\"\u003ch2 id=\\\"seo-giris\\\"\u003e\u003cspan class=\\\"relative inline-block font-black text-[#4b4ee6] after:absolute after:inset-x-0 after:-bottom-1 after:h-2 after:rounded-full after:bg-[#5E61FF]/14 after:content-['']\\\"\u003e\u003cspan class=\\\"relative z-10\\\"\u003e9. Sınıf\u003c/span\u003e\u003c/span\u003e EBOB-EKOK Testleri\u003c/h2\u003e\u003cp\u003eEBOB-EKOK testleri; en büyük ortak bölen, en küçük ortak kat, asal çarpanlara ayırma ve günlük yaşam problemlerinde ortak bölen-kat kullanımını pekiştirir.\u003c/p\u003e\u003ch2\u003eEBOB ve EKOK Farkı\u003c/h2\u003e\u003cp\u003eEBOB ortak bölenlerin en büyüğüdür ve parçalama, paylaştırma, en büyük eş parça problemlerinde kullanılır. EKOK ortak katların en küçüğüdür ve tekrar eden olayların birlikte gerçekleşme zamanını bulmada kullanılır.\u003c/p\u003e\u003ch2\u003eProblem Stratejisi\u003c/h2\u003e\u003cp\u003eSoruda eşit parçalara ayırma, en büyük parça veya bölüştürme varsa EBOB; birlikte tekrar etme, karşılaşma veya ortak zaman varsa EKOK düşünülmelidir.\u003c/p\u003e\"}}]}],[\"$\",\"$L1b\",\"19496\",{\"data\":{\"testIds\":[6412,6413,6414,6415,6416,6417,6418,6419,6420,6421],\"pageSize\":10,\"contentKey\":\"9-sinif-matematik-ebob-ekok-tests\",\"titleOverride\":\"9. Sınıf Matematik Ebob Ekok Testleri\"},\"initialResult\":\"$undefined\",\"initialResults\":{\"6416\":{\"test\":{\"id\":6416,\"country_code\":\"tr\",\"locale\":\"tr-TR\",\"slug\":\"9-sinif-matematik-ebob-ekok-test-5\",\"title\":\"9. Sınıf Matematik Ebob Ekok Test 5\",\"description\":\"EBOB-EKOK konusu 5. test.\",\"instructions\":\"Her soruda doğru seçeneği işaretle.\",\"time_limit_seconds\":900},\"questions\":[{\"id\":189340,\"questionOrder\":0,\"questionText\":\"\u003cp\u003eAşağıdaki ifadenin değeri kaçtır?\u003c/p\u003e\u003cp\u003e\u003cmath xmlns=\\\"http://www.w3.org/1998/Math/MathML\\\"\u003e\u003cmrow\u003e\u003cmi\u003eEBOB\u003c/mi\u003e\u003cmo\u003e(\u003c/mo\u003e\u003cmn\u003e36\u003c/mn\u003e\u003cmo\u003e,\u003c/mo\u003e\u003cmn\u003e60\u003c/mn\u003e\u003cmo\u003e)\u003c/mo\u003e\u003cmo\u003e+\u003c/mo\u003e\u003cmi\u003eEKOK\u003c/mi\u003e\u003cmo\u003e(\u003c/mo\u003e\u003cmn\u003e36\u003c/mn\u003e\u003cmo\u003e,\u003c/mo\u003e\u003cmn\u003e60\u003c/mn\u003e\u003cmo\u003e)\u003c/mo\u003e\u003c/mrow\u003e\u003c/math\u003e\u003c/p\u003e\",\"explanationHtml\":\"$1c\",\"solutionSummary\":\"İfadede iki sayı için EBOB ve EKOK isteniyor. a = 36, b = 60 Önce asal çarpanlarına ayıralım. 36 = 2 2 \u0026#x00D7; 3 2 60 = 2 2 \u0026#x00D7; 3 \u0026#x00D7; 5 EBOB: ortak asal çarpanların küçük üsleri alınır. EBOB ( 36, 60 ) = 2 2 \u0026#x00D7; 3 = 12 EKOK: asal çarpanların büyük üsleri alınır. EKOK ( 36, 60 ) = 2 2 \u0026#x00D7; 3 2 \u0026#x00D7; 5 = 180 İstenen toplamı bulalım. EBOB ( 36, 60 ) + EKOK ( 36, 60 ) = 12 + 180 = 192 Sonuç 192 olduğundan doğru cevap A428 şıkkıdır.\",\"solutionSteps\":[{\"text\":\"İfadede iki sayı için EBOB ve EKOK isteniyor. a = 36, b = 60 Önce asal çarpanlarına ayıralım. 36 = 2 2 \u0026#x00D7; 3 2 60 = 2 2 \u0026#x00D7; 3 \u0026#x00D7; 5 EBOB: ortak asal çarpanların küçük üsleri alınır. EBOB ( 36, 60 ) = 2 2 \u0026#x00D7; 3 = 12 EKOK: asal çarpanların büyük üsleri alınır. EKOK ( 36, 60 ) = 2 2 \u0026#x00D7; 3 2 \u0026#x00D7; 5 = 180 İstenen toplamı bulalım. EBOB ( 36, 60 ) + EKOK ( 36, 60 ) = 12 + 180 = 192 Sonuç 192 olduğundan doğru cevap A428 şıkkıdır.\",\"title\":\"Çözüm\"}],\"optionExplanations\":{},\"correctOptionKey\":\"A\",\"options\":[{\"id\":757315,\"key\":\"A\",\"text\":\"\u003cmath xmlns=\\\"http://www.w3.org/1998/Math/MathML\\\"\u003e\u003cmn\u003e192\u003c/mn\u003e\u003c/math\u003e\"},{\"id\":757314,\"key\":\"B\",\"text\":\"\u003cmath xmlns=\\\"http://www.w3.org/1998/Math/MathML\\\"\u003e\u003cmn\u003e180\u003c/mn\u003e\u003c/math\u003e\"},{\"id\":757313,\"key\":\"C\",\"text\":\"\u003cmath xmlns=\\\"http://www.w3.org/1998/Math/MathML\\\"\u003e\u003cmn\u003e168\u003c/mn\u003e\u003c/math\u003e\"},{\"id\":757316,\"key\":\"D\",\"text\":\"\u003cmath xmlns=\\\"http://www.w3.org/1998/Math/MathML\\\"\u003e\u003cmn\u003e204\u003c/mn\u003e\u003c/math\u003e\"}]},{\"id\":189341,\"questionOrder\":1,\"questionText\":\"\u003cp\u003ePozitif tam sayılar için\u003c/p\u003e\u003cp\u003e\u003cmath\u003e\u003cmtext\u003eEBOB\u003c/mtext\u003e\u003cmo\u003e(\u003c/mo\u003e\u003cmi\u003ea\u003c/mi\u003e\u003cmo\u003e,\u003c/mo\u003e\u003cmi\u003eb\u003c/mi\u003e\u003cmo\u003e)\u003c/mo\u003e\u003cmo\u003e=\u003c/mo\u003e\u003cmn\u003e18\u003c/mn\u003e\u003c/math\u003e, \u003cmath\u003e\u003cmtext\u003eEKOK\u003c/mtext\u003e\u003cmo\u003e(\u003c/mo\u003e\u003cmi\u003ea\u003c/mi\u003e\u003cmo\u003e,\u003c/mo\u003e\u003cmi\u003eb\u003c/mi\u003e\u003cmo\u003e)\u003c/mo\u003e\u003cmo\u003e=\u003c/mo\u003e\u003cmn\u003e360\u003c/mn\u003e\u003c/math\u003e, \u003cmath\u003e\u003cmn\u003e24\u003c/mn\u003e\u003cmo\u003e|\u003c/mo\u003e\u003cmi\u003ea\u003c/mi\u003e\u003c/math\u003e ve \u003cmath\u003e\u003cmi\u003ea\u003c/mi\u003e\u003cmo\u003e\u0026lt;\u003c/mo\u003e\u003cmi\u003eb\u003c/mi\u003e\u003c/math\u003e koşulları sağlanıyor.\u003c/p\u003e\u003cp\u003e\u003cmath\u003e\u003cmi\u003ea\u003c/mi\u003e\u003c/math\u003e kaçtır?\u003c/p\u003e\",\"explanationHtml\":\"$1d\",\"solutionSummary\":\"Verilenler: EBOB ( a, b ) = 18 EKOK ( a, b ) = 360 24 | a a \u003c b EBOB ve EKOK ilişkisini kullanalım: a b = EBOB ( a, b ) \u0026#x00D7; EKOK ( a, b ) a b = 18 \u0026#x00D7; 360 = 6480 EBOB 18 olduğuna göre sayıları 18 çarpanı ile yazalım: a = 18 x b = 18 y Burada EBOB ( x, y ) = 1 EKOK koşulunu yazalım. EBOB 1 olduğu için EKOK ( x, y ) = x y Dolayısıyla EKOK ( a, b ) = 18 x y = 360 x y = 20 Çarpımı 20 olan ve aralarında asal olan ikililer: ( x, y ) = ( 1, 20 ) ( x, y ) = ( 4, 5 ) Ayrıca a \u003c b olduğu için x \u003c y Şimdi 24 bölünebilme koşulunu kullanalım: 24 | a 24 | 18 x Bu, 18 x = 24 k şeklinde yazılabilir. Buradan x = 24 18 k = 4 3 k x tam sayı olacağı için 3 | k olmalı; yani x en az 4’ün katı olmak zorundadır. Listede bu şartı sağlayan tek seçenek x = 4 olur ve buna karşılık y = 5 Sonuç: a = 18 \u0026#x00D7; 4 = 72 Doğru seçenek kontrolü: 72 Bu değer şıklarda B seçeneğidir; yani doğru cevap B’dir.\",\"solutionSteps\":[{\"text\":\"Verilenler: EBOB ( a, b ) = 18 EKOK ( a, b ) = 360 24 | a a \u003c b EBOB ve EKOK ilişkisini kullanalım: a b = EBOB ( a, b ) \u0026#x00D7; EKOK ( a, b ) a b = 18 \u0026#x00D7; 360 = 6480 EBOB 18 olduğuna göre sayıları 18 çarpanı ile yazalım: a = 18 x b = 18 y Burada EBOB ( x, y ) = 1 EKOK koşulunu yazalım. EBOB 1 olduğu için EKOK ( x, y ) = x y Dolayısıyla EKOK ( a, b ) = 18 x y = 360 x y = 20 Çarpımı 20 olan ve aralarında asal olan ikililer: ( x, y ) = ( 1, 20 ) ( x, y ) = ( 4, 5 ) Ayrıca a \u003c b olduğu için x \u003c y Şimdi 24 bölünebilme koşulunu kullanalım: 24 | a 24 | 18 x Bu, 18 x = 24 k şeklinde yazılabilir. Buradan x = 24 18 k = 4 3 k x tam sayı olacağı için 3 | k olmalı; yani x en az 4’ün katı olmak zorundadır. Listede bu şartı sağlayan tek seçenek x = 4 olur ve buna karşılık y = 5 Sonuç: a = 18 \u0026#x00D7; 4 = 72 Doğru seçenek kontrolü: 72 Bu değer şıklarda B seçeneğidir; yani doğru cevap B’dir.\",\"title\":\"Çözüm\"}],\"optionExplanations\":{},\"correctOptionKey\":\"B\",\"options\":[{\"id\":757317,\"key\":\"A\",\"text\":\"\u003cmath\u003e\u003cmn\u003e90\u003c/mn\u003e\u003c/math\u003e\"},{\"id\":757318,\"key\":\"B\",\"text\":\"\u003cmath\u003e\u003cmn\u003e72\u003c/mn\u003e\u003c/math\u003e\"},{\"id\":757319,\"key\":\"C\",\"text\":\"\u003cmath\u003e\u003cmn\u003e120\u003c/mn\u003e\u003c/math\u003e\"},{\"id\":757320,\"key\":\"D\",\"text\":\"\u003cmath\u003e\u003cmn\u003e360\u003c/mn\u003e\u003c/math\u003e\"}]},{\"id\":189342,\"questionOrder\":2,\"questionText\":\"\u003cp\u003eAşağıdaki işlemin sonucu kaçtır?\u003c/p\u003e\u003cp\u003e\u003cmath\u003e\u003cmi\u003eEBOB\u003c/mi\u003e\u003cmo\u003e(\u003c/mo\u003e\u003cmn\u003e24\u003c/mn\u003e\u003cmo\u003e,\u003c/mo\u003e\u003cmn\u003e36\u003c/mn\u003e\u003cmo\u003e)\u003c/mo\u003e\u003cmo\u003e+\u003c/mo\u003e\u003cmi\u003eEKOK\u003c/mi\u003e\u003cmo\u003e(\u003c/mo\u003e\u003cmn\u003e24\u003c/mn\u003e\u003cmo\u003e,\u003c/mo\u003e\u003cmn\u003e36\u003c/mn\u003e\u003cmo\u003e)\u003c/mo\u003e\u003c/math\u003e\u003c/p\u003e\",\"explanationHtml\":\"$1e\",\"solutionSummary\":\"İstenen ifade: EBOB ( 24, 36 ) + EKOK ( 24, 36 ) Önce sayıları asal çarpanlarına ayıralım: 24 = 2 3 · 3 36 = 2 2 · 3 2 EBOB için ortak asal çarpanların üslerinin küçüğünü alırız: EBOB ( 24, 36 ) = 2 2 · 3 1 = 12 EKOK için asal çarpanların üslerinin büyüğünü alırız: EKOK ( 24, 36 ) = 2 3 · 3 2 = 72 Toplayalım: EBOB ( 24, 36 ) + EKOK ( 24, 36 ) = 12 + 72 = 84 Doğru seçenek: C360\",\"solutionSteps\":[{\"text\":\"İstenen ifade: EBOB ( 24, 36 ) + EKOK ( 24, 36 ) Önce sayıları asal çarpanlarına ayıralım: 24 = 2 3 · 3 36 = 2 2 · 3 2 EBOB için ortak asal çarpanların üslerinin küçüğünü alırız: EBOB ( 24, 36 ) = 2 2 · 3 1 = 12 EKOK için asal çarpanların üslerinin büyüğünü alırız: EKOK ( 24, 36 ) = 2 3 · 3 2 = 72 Toplayalım: EBOB ( 24, 36 ) + EKOK ( 24, 36 ) = 12 + 72 = 84 Doğru seçenek: C360\",\"title\":\"Çözüm\"}],\"optionExplanations\":{},\"correctOptionKey\":\"C\",\"options\":[{\"id\":757321,\"key\":\"A\",\"text\":\"\u003cmath\u003e\u003cmn\u003e72\u003c/mn\u003e\u003c/math\u003e\"},{\"id\":757323,\"key\":\"B\",\"text\":\"\u003cmath\u003e\u003cmn\u003e96\u003c/mn\u003e\u003c/math\u003e\"},{\"id\":757322,\"key\":\"C\",\"text\":\"\u003cmath\u003e\u003cmn\u003e84\u003c/mn\u003e\u003c/math\u003e\"},{\"id\":757324,\"key\":\"D\",\"text\":\"\u003cmath\u003e\u003cmn\u003e60\u003c/mn\u003e\u003c/math\u003e\"}]},{\"id\":189343,\"questionOrder\":3,\"questionText\":\"\u003cp\u003eAşağıda iki pozitif tam sayı için verilen bilgilere göre diğer sayıyı bulun.\u003c/p\u003e\u003cp\u003e\u003cmath xmlns=\\\"http://www.w3.org/1998/Math/MathML\\\"\u003e\u003cmrow\u003e\u003cmi\u003eEBOB\u003c/mi\u003e\u003cmo\u003e(\u003c/mo\u003e\u003cmi\u003ea\u003c/mi\u003e\u003cmo\u003e,\u003c/mo\u003e\u003cmi\u003eb\u003c/mi\u003e\u003cmo\u003e)\u003c/mo\u003e\u003cmo\u003e=\u003c/mo\u003e\u003cmn\u003e6\u003c/mn\u003e\u003c/mrow\u003e\u003c/math\u003e\u003c/p\u003e\u003cp\u003e\u003cmath xmlns=\\\"http://www.w3.org/1998/Math/MathML\\\"\u003e\u003cmrow\u003e\u003cmi\u003eEKOK\u003c/mi\u003e\u003cmo\u003e(\u003c/mo\u003e\u003cmi\u003ea\u003c/mi\u003e\u003cmo\u003e,\u003c/mo\u003e\u003cmi\u003eb\u003c/mi\u003e\u003cmo\u003e)\u003c/mo\u003e\u003cmo\u003e=\u003c/mo\u003e\u003cmn\u003e180\u003c/mn\u003e\u003c/mrow\u003e\u003c/math\u003e\u003c/p\u003e\u003cp\u003e\u003cmath xmlns=\\\"http://www.w3.org/1998/Math/MathML\\\"\u003e\u003cmrow\u003e\u003cmi\u003ea\u003c/mi\u003e\u003cmo\u003e=\u003c/mo\u003e\u003cmn\u003e30\u003c/mn\u003e\u003c/mrow\u003e\u003c/math\u003e\u003c/p\u003e\u003cp\u003e\u003cmath xmlns=\\\"http://www.w3.org/1998/Math/MathML\\\"\u003e\u003cmrow\u003e\u003cmi\u003eb\u003c/mi\u003e\u003cmo\u003e=\u003c/mo\u003e\u003cmo\u003e?\u003c/mo\u003e\u003c/mrow\u003e\u003c/math\u003e\u003c/p\u003e\",\"explanationHtml\":\"$1f\",\"solutionSummary\":\"Doğru seçenek D ’dir. İki pozitif tam sayı için temel bağıntı: EBOB ( a, b ) \u0026#x22C5; EKOK ( a, b ) = a \u0026#x22C5; b Verilenleri yerine yazalım: 6 \u0026#x22C5; 180 = 30 \u0026#x22C5; b Sol tarafı hesaplayalım: 6 \u0026#x22C5; 180 = 1080 Eşitliği düzenleyelim: 1080 = 30 \u0026#x22C5; b Her iki tarafı 30 ’a bölelim: b = 1080 30 Sonuç: b = 36\",\"solutionSteps\":[{\"text\":\"Doğru seçenek D ’dir. İki pozitif tam sayı için temel bağıntı: EBOB ( a, b ) \u0026#x22C5; EKOK ( a, b ) = a \u0026#x22C5; b Verilenleri yerine yazalım: 6 \u0026#x22C5; 180 = 30 \u0026#x22C5; b Sol tarafı hesaplayalım: 6 \u0026#x22C5; 180 = 1080 Eşitliği düzenleyelim: 1080 = 30 \u0026#x22C5; b Her iki tarafı 30 ’a bölelim: b = 1080 30 Sonuç: b = 36\",\"title\":\"Çözüm\"}],\"optionExplanations\":{},\"correctOptionKey\":\"D\",\"options\":[{\"id\":757325,\"key\":\"A\",\"text\":\"\u003cmath xmlns=\\\"http://www.w3.org/1998/Math/MathML\\\"\u003e\u003cmn\u003e24\u003c/mn\u003e\u003c/math\u003e\"},{\"id\":757328,\"key\":\"B\",\"text\":\"\u003cmath xmlns=\\\"http://www.w3.org/1998/Math/MathML\\\"\u003e\u003cmn\u003e54\u003c/mn\u003e\u003c/math\u003e\"},{\"id\":757327,\"key\":\"C\",\"text\":\"\u003cmath xmlns=\\\"http://www.w3.org/1998/Math/MathML\\\"\u003e\u003cmn\u003e42\u003c/mn\u003e\u003c/math\u003e\"},{\"id\":757326,\"key\":\"D\",\"text\":\"\u003cmath xmlns=\\\"http://www.w3.org/1998/Math/MathML\\\"\u003e\u003cmn\u003e36\u003c/mn\u003e\u003c/math\u003e\"}]},{\"id\":189344,\"questionOrder\":4,\"questionText\":\"\u003cp\u003eAşağıdaki sayılar için \u003cb\u003eEKOK\u003c/b\u003e değeri kaçtır?\u003c/p\u003e\u003cmath xmlns=\\\"http://www.w3.org/1998/Math/MathML\\\"\u003e\u003cmtext\u003eEKOK\u003c/mtext\u003e\u003cmo\u003e(\u003c/mo\u003e\u003cmn\u003e24\u003c/mn\u003e\u003cmo\u003e,\u003c/mo\u003e\u003cmn\u003e36\u003c/mn\u003e\u003cmo\u003e)\u003c/mo\u003e\u003c/math\u003e\",\"explanationHtml\":\"$20\",\"solutionSummary\":\"Soruda istenen değer, verilen iki sayının EKOK’udur. Şıkları kontrol etmek için EKOK’u asal çarpanlara ayırarak bulalım. Verilen sayılar: 24, 36 Asal çarpanlarına ayıralım: 24 = 2 3 · 3 36 = 2 2 · 3 2 EKOK alınırken her asal çarpanın kuvveti, iki sayıdaki en büyük kuvvet olarak seçilir: EKOK ( 24, 36 ) = 2 3 · 3 2 Çarpımı hesaplayalım: 2 3 · 3 2 = 8 · 9 = 72 Buna göre doğru cevap A371 şıkkıdır. EKOK ( 24, 36 ) = 72\",\"solutionSteps\":[{\"text\":\"Soruda istenen değer, verilen iki sayının EKOK’udur. Şıkları kontrol etmek için EKOK’u asal çarpanlara ayırarak bulalım. Verilen sayılar: 24, 36 Asal çarpanlarına ayıralım: 24 = 2 3 · 3 36 = 2 2 · 3 2 EKOK alınırken her asal çarpanın kuvveti, iki sayıdaki en büyük kuvvet olarak seçilir: EKOK ( 24, 36 ) = 2 3 · 3 2 Çarpımı hesaplayalım: 2 3 · 3 2 = 8 · 9 = 72 Buna göre doğru cevap A371 şıkkıdır. EKOK ( 24, 36 ) = 72\",\"title\":\"Çözüm\"}],\"optionExplanations\":{},\"correctOptionKey\":\"A\",\"options\":[{\"id\":757331,\"key\":\"A\",\"text\":\"\u003cmath xmlns=\\\"http://www.w3.org/1998/Math/MathML\\\"\u003e\u003cmn\u003e72\u003c/mn\u003e\u003c/math\u003e\"},{\"id\":757330,\"key\":\"B\",\"text\":\"\u003cmath xmlns=\\\"http://www.w3.org/1998/Math/MathML\\\"\u003e\u003cmn\u003e36\u003c/mn\u003e\u003c/math\u003e\"},{\"id\":757329,\"key\":\"C\",\"text\":\"\u003cmath xmlns=\\\"http://www.w3.org/1998/Math/MathML\\\"\u003e\u003cmn\u003e12\u003c/mn\u003e\u003c/math\u003e\"},{\"id\":757332,\"key\":\"D\",\"text\":\"\u003cmath xmlns=\\\"http://www.w3.org/1998/Math/MathML\\\"\u003e\u003cmn\u003e144\u003c/mn\u003e\u003c/math\u003e\"}]},{\"id\":189345,\"questionOrder\":5,\"questionText\":\"\u003cdiv\u003ePozitif tamsayılar \u003cmath\u003e\u003cmi\u003ea\u003c/mi\u003e\u003c/math\u003e ve \u003cmath\u003e\u003cmi\u003eb\u003c/mi\u003e\u003c/math\u003e için \u003cmath\u003e\u003cmi\u003eEBOB\u003c/mi\u003e\u003cmfenced\u003e\u003cmi\u003ea\u003c/mi\u003e\u003cmo\u003e,\u003c/mo\u003e\u003cmi\u003eb\u003c/mi\u003e\u003c/mfenced\u003e\u003cmo\u003e=\u003c/mo\u003e\u003cmn\u003e24\u003c/mn\u003e\u003c/math\u003e ve \u003cmath\u003e\u003cmi\u003eEKOK\u003c/mi\u003e\u003cmfenced\u003e\u003cmi\u003ea\u003c/mi\u003e\u003cmo\u003e,\u003c/mo\u003e\u003cmi\u003eb\u003c/mi\u003e\u003c/mfenced\u003e\u003cmo\u003e=\u003c/mo\u003e\u003cmn\u003e1680\u003c/mn\u003e\u003c/math\u003e veriliyor. Ayrıca \u003cmath\u003e\u003cmi\u003ea\u003c/mi\u003e\u003cmo\u003e\u0026lt;\u003c/mo\u003e\u003cmi\u003eb\u003c/mi\u003e\u003c/math\u003e ve \u003cmath\u003e\u003cmn\u003e7\u003c/mn\u003e\u003cmo\u003e\u0026#x2223;\u003c/mo\u003e\u003cmi\u003ea\u003c/mi\u003e\u003c/math\u003e. Buna göre \u003cmath\u003e\u003cmi\u003eb\u003c/mi\u003e\u003c/math\u003e kaçtır?\u003c/div\u003e\",\"explanationHtml\":\"$21\",\"solutionSummary\":\"Verilenler: EBOB a, b = 24 EKOK a, b = 1680 a \u003c b 7 \u0026#x2223; a 1) EBOB–EKOK bağıntısını kullanalım: a \u0026#x22C5; b = EBOB a, b \u0026#x22C5; EKOK a, b a \u0026#x22C5; b = 24 \u0026#x22C5; 1680 = 40320 2) EBOB 24 olduğuna göre sayıları 24 ile çarpım şeklinde yazalım: a = 24 x b = 24 y EBOB x, y = 1 3) EKOK bilgisini kullanalım. EBOB(x,y)=1 iken EKOK(x,y)=x·y olur: EKOK a, b = 24 \u0026#x22C5; x \u0026#x22C5; y 1680 = 24 x y x y = 1680 24 = 70 4) 7 | a koşulunu x üzerinden yazalım: 7 \u0026#x2223; a = 24 x 7 \u0026#x2223; x 5) x·y=70 ve EBOB(x,y)=1 olduğundan, 70’in asal çarpanlarını paylaştırırken ortak asal çarpan olmamalı: 70 = 2 \u0026#x22C5; 5 \u0026#x22C5; 7 6) 7 | x olmalı. Uygun (aralarında asal) çarpan çiftlerini deneyelim: x = 7 \u0026#x21D2; y = 10, EBOB 7, 10 = 1 x = 14 \u0026#x21D2; y = 5, EBOB 14, 5 = 1 7) a\u003cb şartını kontrol edelim. a=24x ve b=24y olduğundan x\u003cy olmalı: x = 7 \u003c 10 = y \u0026#x2713; x = 14 \u003e 5 = y \u0026#x2717; 8) O hâlde x=7, y=10: a = 24 \u0026#x22C5; 7 = 168 b = 24 \u0026#x22C5; 10 = 240 Sonuç: Doğru cevap B şıkkıdır.\",\"solutionSteps\":[{\"text\":\"Verilenler: EBOB a, b = 24 EKOK a, b = 1680 a \u003c b 7 \u0026#x2223; a 1) EBOB–EKOK bağıntısını kullanalım: a \u0026#x22C5; b = EBOB a, b \u0026#x22C5; EKOK a, b a \u0026#x22C5; b = 24 \u0026#x22C5; 1680 = 40320 2) EBOB 24 olduğuna göre sayıları 24 ile çarpım şeklinde yazalım: a = 24 x b = 24 y EBOB x, y = 1 3) EKOK bilgisini kullanalım. EBOB(x,y)=1 iken EKOK(x,y)=x·y olur: EKOK a, b = 24 \u0026#x22C5; x \u0026#x22C5; y 1680 = 24 x y x y = 1680 24 = 70 4) 7 | a koşulunu x üzerinden yazalım: 7 \u0026#x2223; a = 24 x 7 \u0026#x2223; x 5) x·y=70 ve EBOB(x,y)=1 olduğundan, 70’in asal çarpanlarını paylaştırırken ortak asal çarpan olmamalı: 70 = 2 \u0026#x22C5; 5 \u0026#x22C5; 7 6) 7 | x olmalı. Uygun (aralarında asal) çarpan çiftlerini deneyelim: x = 7 \u0026#x21D2; y = 10, EBOB 7, 10 = 1 x = 14 \u0026#x21D2; y = 5, EBOB 14, 5 = 1 7) a\u003cb şartını kontrol edelim. a=24x ve b=24y olduğundan x\u003cy olmalı: x = 7 \u003c 10 = y \u0026#x2713; x = 14 \u003e 5 = y \u0026#x2717; 8) O hâlde x=7, y=10: a = 24 \u0026#x22C5; 7 = 168 b = 24 \u0026#x22C5; 10 = 240 Sonuç: Doğru cevap B şıkkıdır.\",\"title\":\"Çözüm\"}],\"optionExplanations\":{},\"correctOptionKey\":\"B\",\"options\":[{\"id\":757333,\"key\":\"A\",\"text\":\"\u003cmath\u003e\u003cmn\u003e168\u003c/mn\u003e\u003c/math\u003e\"},{\"id\":757334,\"key\":\"B\",\"text\":\"\u003cmath\u003e\u003cmn\u003e240\u003c/mn\u003e\u003c/math\u003e\"},{\"id\":757335,\"key\":\"C\",\"text\":\"\u003cmath\u003e\u003cmn\u003e336\u003c/mn\u003e\u003c/math\u003e\"},{\"id\":757336,\"key\":\"D\",\"text\":\"\u003cmath\u003e\u003cmn\u003e420\u003c/mn\u003e\u003c/math\u003e\"}]},{\"id\":189346,\"questionOrder\":6,\"questionText\":\"\u003cp\u003e\u003cmath\u003e\u003cmi\u003eEBOB\u003c/mi\u003e\u003cmo\u003e=\u003c/mo\u003e\u003cmn\u003e12\u003c/mn\u003e\u003c/math\u003e ve \u003cmath\u003e\u003cmi\u003eEKOK\u003c/mi\u003e\u003cmo\u003e=\u003c/mo\u003e\u003cmn\u003e180\u003c/mn\u003e\u003c/math\u003e olan iki sayının biri \u003cmath\u003e\u003cmn\u003e60\u003c/mn\u003e\u003c/math\u003e ise diğeri kaçtır?\u003c/p\u003e\",\"explanationHtml\":\"$22\",\"solutionSummary\":\"Verilenlere göre iki sayı a ve b olsun. Bilinen bağıntı: a \u0026#x00D7; b = EBOB \u0026#x00D7; EKOK Değerleri yerine yazalım: a \u0026#x00D7; b = 12 \u0026#x00D7; 180 Çarpımı hesaplayalım: a \u0026#x00D7; b = 2160 Sayıların birinin 60 olduğu verilmiş. O hâlde: 60 \u0026#x00D7; x = 2160 Diğer sayıyı bulmak için bölelim: x = 2160 60 = 36 Bulunan değer 36 olduğundan doğru seçenek C 'dir; yani C doğru.\",\"solutionSteps\":[{\"text\":\"Verilenlere göre iki sayı a ve b olsun. Bilinen bağıntı: a \u0026#x00D7; b = EBOB \u0026#x00D7; EKOK Değerleri yerine yazalım: a \u0026#x00D7; b = 12 \u0026#x00D7; 180 Çarpımı hesaplayalım: a \u0026#x00D7; b = 2160 Sayıların birinin 60 olduğu verilmiş. O hâlde: 60 \u0026#x00D7; x = 2160 Diğer sayıyı bulmak için bölelim: x = 2160 60 = 36 Bulunan değer 36 olduğundan doğru seçenek C 'dir; yani C doğru.\",\"title\":\"Çözüm\"}],\"optionExplanations\":{},\"correctOptionKey\":\"C\",\"options\":[{\"id\":757337,\"key\":\"A\",\"text\":\"\u003cmath\u003e\u003cmn\u003e24\u003c/mn\u003e\u003c/math\u003e\"},{\"id\":757338,\"key\":\"B\",\"text\":\"\u003cmath\u003e\u003cmn\u003e30\u003c/mn\u003e\u003c/math\u003e\"},{\"id\":757339,\"key\":\"C\",\"text\":\"\u003cmath\u003e\u003cmn\u003e36\u003c/mn\u003e\u003c/math\u003e\"},{\"id\":757340,\"key\":\"D\",\"text\":\"\u003cmath\u003e\u003cmn\u003e48\u003c/mn\u003e\u003c/math\u003e\"}]},{\"id\":189347,\"questionOrder\":7,\"questionText\":\"\u003cp\u003e\u003cmath\u003e\u003cmrow\u003e\u003cmi\u003ea\u003c/mi\u003e\u003c/mrow\u003e\u003c/math\u003e ve \u003cmath\u003e\u003cmrow\u003e\u003cmi\u003eb\u003c/mi\u003e\u003c/mrow\u003e\u003c/math\u003e pozitif tam sayıları için \u003cmath\u003e\u003cmrow\u003e\u003cmi\u003eEBOB\u003c/mi\u003e\u003cmo\u003e(\u003c/mo\u003e\u003cmi\u003ea\u003c/mi\u003e\u003cmo\u003e,\u003c/mo\u003e\u003cmi\u003eb\u003c/mi\u003e\u003cmo\u003e)\u003c/mo\u003e\u003cmo\u003e=\u003c/mo\u003e\u003cmn\u003e18\u003c/mn\u003e\u003c/mrow\u003e\u003c/math\u003e ve \u003cmath\u003e\u003cmrow\u003e\u003cmi\u003eEKOK\u003c/mi\u003e\u003cmo\u003e(\u003c/mo\u003e\u003cmi\u003ea\u003c/mi\u003e\u003cmo\u003e,\u003c/mo\u003e\u003cmi\u003eb\u003c/mi\u003e\u003cmo\u003e)\u003c/mo\u003e\u003cmo\u003e=\u003c/mo\u003e\u003cmn\u003e1260\u003c/mn\u003e\u003c/mrow\u003e\u003c/math\u003e veriliyor. Buna göre \u003cmath\u003e\u003cmrow\u003e\u003cmi\u003ea\u003c/mi\u003e\u003cmo\u003e+\u003c/mo\u003e\u003cmi\u003eb\u003c/mi\u003e\u003c/mrow\u003e\u003c/math\u003e ifadesinin alabileceği en küçük değer kaçtır?\u003c/p\u003e\",\"explanationHtml\":\"$23\",\"solutionSummary\":\"Verilenler: EBOB ( a, b ) = 18 EKOK ( a, b ) = 1260 Bilinen bağıntı: a ⋅ b = EBOB ( a, b ) ⋅ EKOK ( a, b ) Buradan: a ⋅ b = 18 ⋅ 1260 = 22680 Ortak böleni ayıralım: a = 18 x b = 18 y Bu durumda: EBOB ( x, y ) = 1 EKOK bağıntısını kullanalım: EKOK ( a, b ) = 18 x y Verilen EKOK değerini yazınca: 18 x y = 1260 x y = 70 Şimdi EBOB ( x, y ) = 1 şartıyla x y = 70 çarpan çiftlerini yazalım (aralarında asal olanlar): ( 1, 70 ) ( 2, 35 ) ( 5, 14 ) ( 7, 10 ) Toplam: a + b = 18 x + 18 y = 18 ( x + y ) En küçük toplam için x + y en küçük olmalı. Yukarıdaki çiftlerde en küçük toplam: 7 + 10 = 17 Dolayısıyla: a + b = 18 ⋅ 17 = 306 Sonuç: En küçük değer 306 olur. Bu da  şıkkıD664dır; yani B doğru.\",\"solutionSteps\":[{\"text\":\"Verilenler: EBOB ( a, b ) = 18 EKOK ( a, b ) = 1260 Bilinen bağıntı: a ⋅ b = EBOB ( a, b ) ⋅ EKOK ( a, b ) Buradan: a ⋅ b = 18 ⋅ 1260 = 22680 Ortak böleni ayıralım: a = 18 x b = 18 y Bu durumda: EBOB ( x, y ) = 1 EKOK bağıntısını kullanalım: EKOK ( a, b ) = 18 x y Verilen EKOK değerini yazınca: 18 x y = 1260 x y = 70 Şimdi EBOB ( x, y ) = 1 şartıyla x y = 70 çarpan çiftlerini yazalım (aralarında asal olanlar): ( 1, 70 ) ( 2, 35 ) ( 5, 14 ) ( 7, 10 ) Toplam: a + b = 18 x + 18 y = 18 ( x + y ) En küçük toplam için x + y en küçük olmalı. Yukarıdaki çiftlerde en küçük toplam: 7 + 10 = 17 Dolayısıyla: a + b = 18 ⋅ 17 = 306 Sonuç: En küçük değer 306 olur. Bu da  şıkkıD664dır; yani B doğru.\",\"title\":\"Çözüm\"}],\"optionExplanations\":{},\"correctOptionKey\":\"D\",\"options\":[{\"id\":757341,\"key\":\"A\",\"text\":\"\u003cmath\u003e\u003cmn\u003e342\u003c/mn\u003e\u003c/math\u003e\"},{\"id\":757344,\"key\":\"B\",\"text\":\"\u003cmath\u003e\u003cmn\u003e666\u003c/mn\u003e\u003c/math\u003e\"},{\"id\":757343,\"key\":\"C\",\"text\":\"\u003cmath\u003e\u003cmn\u003e324\u003c/mn\u003e\u003c/math\u003e\"},{\"id\":757342,\"key\":\"D\",\"text\":\"\u003cmath\u003e\u003cmn\u003e306\u003c/mn\u003e\u003c/math\u003e\"}]},{\"id\":189348,\"questionOrder\":8,\"questionText\":\"\u003cp\u003e\u003cmath\u003e\u003cmrow\u003e\u003cmi\u003eEBOB\u003c/mi\u003e\u003cmo stretchy=\\\"false\\\"\u003e(\u003c/mo\u003e\u003cmn\u003e36\u003c/mn\u003e\u003cmo\u003e,\u003c/mo\u003e\u003cmn\u003e48\u003c/mn\u003e\u003cmo stretchy=\\\"false\\\"\u003e)\u003c/mo\u003e\u003cmo\u003e+\u003c/mo\u003e\u003cmi\u003eEKOK\u003c/mi\u003e\u003cmo stretchy=\\\"false\\\"\u003e(\u003c/mo\u003e\u003cmn\u003e36\u003c/mn\u003e\u003cmo\u003e,\u003c/mo\u003e\u003cmn\u003e48\u003c/mn\u003e\u003cmo stretchy=\\\"false\\\"\u003e)\u003c/mo\u003e\u003c/mrow\u003e\u003c/math\u003e işleminin sonucu kaçtır?\u003c/p\u003e\",\"explanationHtml\":\"$24\",\"solutionSummary\":\"İşlem: EBOB ( 36, 48 ) + EKOK ( 36, 48 ) Önce sayıları asal çarpanlarına ayıralım: 36 = 2 2 · 3 2 48 = 2 4 · 3 EBOB, ortak asal çarpanların üslerinin küçük olanları alınarak bulunur: EBOB ( 36, 48 ) = 2 2 · 3 = 12 EKOK, asal çarpanların üslerinin büyük olanları alınarak bulunur: EKOK ( 36, 48 ) = 2 4 · 3 2 = 16 · 9 = 144 Şimdi toplamı hesaplayalım: EBOB ( 36, 48 ) + EKOK ( 36, 48 ) = 12 + 144 = 156 Sonuç 156 olduğundan doğru seçenek A423 ’dir.\",\"solutionSteps\":[{\"text\":\"İşlem: EBOB ( 36, 48 ) + EKOK ( 36, 48 ) Önce sayıları asal çarpanlarına ayıralım: 36 = 2 2 · 3 2 48 = 2 4 · 3 EBOB, ortak asal çarpanların üslerinin küçük olanları alınarak bulunur: EBOB ( 36, 48 ) = 2 2 · 3 = 12 EKOK, asal çarpanların üslerinin büyük olanları alınarak bulunur: EKOK ( 36, 48 ) = 2 4 · 3 2 = 16 · 9 = 144 Şimdi toplamı hesaplayalım: EBOB ( 36, 48 ) + EKOK ( 36, 48 ) = 12 + 144 = 156 Sonuç 156 olduğundan doğru seçenek A423 ’dir.\",\"title\":\"Çözüm\"}],\"optionExplanations\":{},\"correctOptionKey\":\"A\",\"options\":[{\"id\":757346,\"key\":\"A\",\"text\":\"\u003cmath\u003e\u003cmn\u003e156\u003c/mn\u003e\u003c/math\u003e\"},{\"id\":757345,\"key\":\"B\",\"text\":\"\u003cmath\u003e\u003cmn\u003e132\u003c/mn\u003e\u003c/math\u003e\"},{\"id\":757347,\"key\":\"C\",\"text\":\"\u003cmath\u003e\u003cmn\u003e168\u003c/mn\u003e\u003c/math\u003e\"},{\"id\":757348,\"key\":\"D\",\"text\":\"\u003cmath\u003e\u003cmn\u003e180\u003c/mn\u003e\u003c/math\u003e\"}]},{\"id\":189349,\"questionOrder\":9,\"questionText\":\"\u003cp\u003e\u003cmath\u003e\u003cmrow\u003e\u003cmi\u003ea\u003c/mi\u003e\u003cmo\u003e,\u003c/mo\u003e\u003cmi\u003eb\u003c/mi\u003e\u003c/mrow\u003e\u003c/math\u003e doğal sayıları için \u003cmath\u003e\u003cmrow\u003e\u003cmtext\u003eEBOB\u003c/mtext\u003e\u003cmo\u003e(\u003c/mo\u003e\u003cmi\u003ea\u003c/mi\u003e\u003cmo\u003e,\u003c/mo\u003e\u003cmi\u003eb\u003c/mi\u003e\u003cmo\u003e)\u003c/mo\u003e\u003cmo\u003e=\u003c/mo\u003e\u003cmn\u003e18\u003c/mn\u003e\u003c/mrow\u003e\u003c/math\u003e ve \u003cmath\u003e\u003cmrow\u003e\u003cmtext\u003eEKOK\u003c/mtext\u003e\u003cmo\u003e(\u003c/mo\u003e\u003cmi\u003ea\u003c/mi\u003e\u003cmo\u003e,\u003c/mo\u003e\u003cmi\u003eb\u003c/mi\u003e\u003cmo\u003e)\u003c/mo\u003e\u003cmo\u003e=\u003c/mo\u003e\u003cmn\u003e540\u003c/mn\u003e\u003c/mrow\u003e\u003c/math\u003e olsun. Ayrıca \u003cmath\u003e\u003cmi\u003ea\u003c/mi\u003e\u003c/math\u003e sayısı \u003cmath\u003e\u003cmn\u003e90\u003c/mn\u003e\u003c/math\u003e ile tam bölünüyor ve \u003cmath\u003e\u003cmrow\u003e\u003cmi\u003ea\u003c/mi\u003e\u003cmo\u003e\u0026lt;\u003c/mo\u003e\u003cmi\u003eb\u003c/mi\u003e\u003c/mrow\u003e\u003c/math\u003e.\u003cbr/\u003eBuna göre \u003cmath\u003e\u003cmrow\u003e\u003cmi\u003eb\u003c/mi\u003e\u003cmo\u003e-\u003c/mo\u003e\u003cmi\u003ea\u003c/mi\u003e\u003c/mrow\u003e\u003c/math\u003e kaçtır?\u003c/p\u003e\",\"explanationHtml\":\"$25\",\"solutionSummary\":\"Verilenler: EBOB ( a, b ) = 18 EKOK ( a, b ) = 540 90 \u0026#x2223; a a \u003c b 1) EBOB–EKOK bağıntısı: a \u0026#x22C5; b = EBOB ( a, b ) \u0026#x22C5; EKOK ( a, b ) a \u0026#x22C5; b = 18 \u0026#x22C5; 540 = 9720 2) EBOB ile sadeleştirme: a = 18 x b = 18 y EBOB ( x, y ) = 1 3) EKOK koşulundan çarpım: EKOK ( a, b ) = 18 x y 18 x y = 540 x y = 30 4) Bölünebilme şartını kullanalım: 90 \u0026#x2223; a 90 \u0026#x2223; 18 x 5 \u0026#x2223; x 5) Şimdi hem çarpım hem aralarında asal olma şartı: x y = 30 EBOB ( x, y ) = 1 5 \u0026#x2223; x Bu koşulları sağlayan uygun çarpan çifti: x = 5, y = 6 EBOB ( 5, 6 ) = 1 6) Buna göre sayılara dönelim ve farkı bulalım: a = 18 \u0026#x22C5; 5 = 90 b = 18 \u0026#x22C5; 6 = 108 a \u003c b b - a = 108 - 90 = 18 Sonuç: Doğru cevap B693 seçeneğidir.\",\"solutionSteps\":[{\"text\":\"Verilenler: EBOB ( a, b ) = 18 EKOK ( a, b ) = 540 90 \u0026#x2223; a a \u003c b 1) EBOB–EKOK bağıntısı: a \u0026#x22C5; b = EBOB ( a, b ) \u0026#x22C5; EKOK ( a, b ) a \u0026#x22C5; b = 18 \u0026#x22C5; 540 = 9720 2) EBOB ile sadeleştirme: a = 18 x b = 18 y EBOB ( x, y ) = 1 3) EKOK koşulundan çarpım: EKOK ( a, b ) = 18 x y 18 x y = 540 x y = 30 4) Bölünebilme şartını kullanalım: 90 \u0026#x2223; a 90 \u0026#x2223; 18 x 5 \u0026#x2223; x 5) Şimdi hem çarpım hem aralarında asal olma şartı: x y = 30 EBOB ( x, y ) = 1 5 \u0026#x2223; x Bu koşulları sağlayan uygun çarpan çifti: x = 5, y = 6 EBOB ( 5, 6 ) = 1 6) Buna göre sayılara dönelim ve farkı bulalım: a = 18 \u0026#x22C5; 5 = 90 b = 18 \u0026#x22C5; 6 = 108 a \u003c b b - a = 108 - 90 = 18 Sonuç: Doğru cevap B693 seçeneğidir.\",\"title\":\"Çözüm\"}],\"optionExplanations\":{},\"correctOptionKey\":\"B\",\"options\":[{\"id\":757350,\"key\":\"A\",\"text\":\"\u003cmath\u003e\u003cmn\u003e126\u003c/mn\u003e\u003c/math\u003e\"},{\"id\":757349,\"key\":\"B\",\"text\":\"\u003cmath\u003e\u003cmn\u003e18\u003c/mn\u003e\u003c/math\u003e\"},{\"id\":757351,\"key\":\"C\",\"text\":\"\u003cmath\u003e\u003cmn\u003e234\u003c/mn\u003e\u003c/math\u003e\"},{\"id\":757352,\"key\":\"D\",\"text\":\"\u003cmath\u003e\u003cmn\u003e522\u003c/mn\u003e\u003c/math\u003e\"}]}],\"totalItems\":10,\"totalPages\":1,\"currentPage\":1,\"limit\":10,\"hasMore\":false}},\"initialActiveTestNumber\":5,\"countryCode\":\"tr\",\"locale\":\"tr-TR\"}],[\"$\",\"section\",null,{\"className\":\"mx-auto max-w-4xl px-4 py-6 sm:px-6 lg:px-8\",\"children\":[[\"$\",\"h2\",null,{\"className\":\"font-display text-2xl font-bold text-slate-950 sm:text-3xl\",\"children\":\"EBOB-EKOK Testleri Hakkında Sık Sorulanlar\"}],[\"$\",\"div\",null,{\"className\":\"mt-4 divide-y divide-slate-200 rounded-lg border border-slate-200 bg-white shadow-sm shadow-slate-950/5\",\"children\":[[\"$\",\"details\",\"EBOB hangi problemlerde kullanılır?\",{\"className\":\"group p-4\",\"children\":[[\"$\",\"summary\",null,{\"className\":\"cursor-pointer list-none text-base font-bold text-slate-950\",\"children\":\"EBOB hangi problemlerde kullanılır?\"}],[\"$\",\"p\",null,{\"className\":\"mt-3 text-sm leading-7 text-slate-600\",\"children\":\"Eşit ve en büyük parçalara ayırma, paylaştırma ve ortak bölen bulma problemlerinde kullanılır.\"}]]}],[\"$\",\"details\",\"EKOK hangi problemlerde kullanılır?\",{\"className\":\"group p-4\",\"children\":[[\"$\",\"summary\",null,{\"className\":\"cursor-pointer list-none text-base font-bold text-slate-950\",\"children\":\"EKOK hangi problemlerde kullanılır?\"}],[\"$\",\"p\",null,{\"className\":\"mt-3 text-sm leading-7 text-slate-600\",\"children\":\"Tekrar eden olayların birlikte ne zaman gerçekleşeceğini bulma problemlerinde kullanılır.\"}]]}],[\"$\",\"details\",\"EBOB ve EKOK nasıl bulunur?\",{\"className\":\"group p-4\",\"children\":[[\"$\",\"summary\",null,{\"className\":\"cursor-pointer list-none text-base font-bold text-slate-950\",\"children\":\"EBOB ve EKOK nasıl bulunur?\"}],[\"$\",\"p\",null,{\"className\":\"mt-3 text-sm leading-7 text-slate-600\",\"children\":\"Sayılar asal çarpanlarına ayrılır; ortak ve farklı çarpanların uygun üsleri kullanılır.\"}]]}]]}]]}]]]}]\n"])

9. Sınıf Matematik Ebob Ekok Testleri

9. Sınıf EBOB-EKOK Testleri

EBOB ve EKOK Farkı

Problem Stratejisi

9. Sınıf Matematik Ebob Ekok Testleri

Aşağıdaki ifadenin değeri kaçtır?
$EBOB (36, 60) + EKOK (36, 60)$

Pozitif tam sayılar için
$EBOB (a, b) = 18$ , $EKOK (a, b) = 360$ , $24 | a$ ve $a < b$ koşulları sağlanıyor.
$a$ kaçtır?

Aşağıdaki işlemin sonucu kaçtır?
$EBOB (24, 36) + EKOK (24, 36)$

Aşağıda iki pozitif tam sayı için verilen bilgilere göre diğer sayıyı bulun.
$EBOB (a, b) = 6$
$EKOK (a, b) = 180$
$a = 30$
$b = ?$

Aşağıdaki sayılar için EKOK değeri kaçtır?
$EKOK (24, 36)$

Pozitif tamsayılar $a$ ve $b$ için $EBOB (a, b) = 24$ ve $EKOK (a, b) = 1680$ veriliyor. Ayrıca $a < b$ ve $7 ∣ a$ . Buna göre $b$ kaçtır?

$EBOB = 12$ ve $EKOK = 180$ olan iki sayının biri $60$ ise diğeri kaçtır?

$a$ ve $b$ pozitif tam sayıları için $EBOB (a, b) = 18$ ve $EKOK (a, b) = 1260$ veriliyor. Buna göre $a + b$ ifadesinin alabileceği en küçük değer kaçtır?

$EBOB (36, 48) + EKOK (36, 48)$ işleminin sonucu kaçtır?

$a, b$ doğal sayıları için $EBOB (a, b) = 18$ ve $EKOK (a, b) = 540$ olsun. Ayrıca $a$ sayısı $90$ ile tam bölünüyor ve $a < b$ .
Buna göre $b - a$ kaçtır?

EBOB-EKOK Testleri Hakkında Sık Sorulanlar

9. Sınıf Matematik Ebob Ekok Testleri

9. Sınıf EBOB-EKOK Testleri

EBOB ve EKOK Farkı

Problem Stratejisi

9. Sınıf Matematik Ebob Ekok Testleri

Aşağıdaki ifadenin değeri kaçtır?EBOB(36,60)+EKOK(36,60)

Pozitif tam sayılar içinEBOB(a,b)=18, EKOK(a,b)=360, 24|a ve a<b koşulları sağlanıyor.a kaçtır?

Aşağıdaki işlemin sonucu kaçtır?EBOB(24,36)+EKOK(24,36)

Aşağıda iki pozitif tam sayı için verilen bilgilere göre diğer sayıyı bulun.EBOB(a,b)=6EKOK(a,b)=180a=30b=?

Aşağıdaki sayılar için EKOK değeri kaçtır?EKOK(24,36)

Pozitif tamsayılar a ve b için EBOBa,b=24 ve EKOKa,b=1680 veriliyor. Ayrıca a<b ve 7∣a. Buna göre b kaçtır?

EBOB=12 ve EKOK=180 olan iki sayının biri 60 ise diğeri kaçtır?

a ve b pozitif tam sayıları için EBOB(a,b)=18 ve EKOK(a,b)=1260 veriliyor. Buna göre a+b ifadesinin alabileceği en küçük değer kaçtır?

EBOB(36,48)+EKOK(36,48) işleminin sonucu kaçtır?

a,b doğal sayıları için EBOB(a,b)=18 ve EKOK(a,b)=540 olsun. Ayrıca a sayısı 90 ile tam bölünüyor ve a<b.Buna göre b-a kaçtır?

EBOB-EKOK Testleri Hakkında Sık Sorulanlar

Aşağıdaki ifadenin değeri kaçtır?
$EBOB (36, 60) + EKOK (36, 60)$

Pozitif tam sayılar için
$EBOB (a, b) = 18$ , $EKOK (a, b) = 360$ , $24 | a$ ve $a < b$ koşulları sağlanıyor.
$a$ kaçtır?

Aşağıdaki işlemin sonucu kaçtır?
$EBOB (24, 36) + EKOK (24, 36)$

Aşağıda iki pozitif tam sayı için verilen bilgilere göre diğer sayıyı bulun.
$EBOB (a, b) = 6$
$EKOK (a, b) = 180$
$a = 30$
$b = ?$

Aşağıdaki sayılar için EKOK değeri kaçtır?
$EKOK (24, 36)$

Pozitif tamsayılar $a$ ve $b$ için $EBOB (a, b) = 24$ ve $EKOK (a, b) = 1680$ veriliyor. Ayrıca $a < b$ ve $7 ∣ a$ . Buna göre $b$ kaçtır?

$EBOB = 12$ ve $EKOK = 180$ olan iki sayının biri $60$ ise diğeri kaçtır?

$a$ ve $b$ pozitif tam sayıları için $EBOB (a, b) = 18$ ve $EKOK (a, b) = 1260$ veriliyor. Buna göre $a + b$ ifadesinin alabileceği en küçük değer kaçtır?

$EBOB (36, 48) + EKOK (36, 48)$ işleminin sonucu kaçtır?

$a, b$ doğal sayıları için $EBOB (a, b) = 18$ ve $EKOK (a, b) = 540$ olsun. Ayrıca $a$ sayısı $90$ ile tam bölünüyor ve $a < b$ .
Buna göre $b - a$ kaçtır?