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Grade 6 Math · Greatest Common Factor

Grade 6 Greatest Common Factor Practice Test

Build Grade 6 Math skills with five 10-question practice tests on factors, prime factorization, greatest common factor, algorithms, and equal-group problems.

Greatest Common Factor Practice Tests

These Grade 6 Math practice tests help students identify the greatest positive factor shared by two or more numbers. Students practice factor pairs, common factors, prime factorization, the Euclidean algorithm, fraction simplification, and equal-group problems involving classroom materials, supplies, teams, and packages.

Skills covered

  • Listing factors and factor pairs
  • Identifying common factors and the greatest common factor
  • Using prime factorization to find the GCF
  • Applying the Euclidean algorithm and checking results
  • Distinguishing factors from multiples and GCF from LCM
  • Simplifying fractions and grouping objects evenly
  • Interpreting GCF in real-world packaging, teams, rows, and equal sets

How to use these practice tests

Start by listing factor pairs or writing each number as a product of primes. Keep only the prime factors shared by all numbers, use the smallest shared exponents, and multiply them. For word problems, explain how the GCF determines the greatest number of equal groups or the greatest equal section size.

For more Grade 6 Math practice, return to the Grade 6 Math category.

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Grade 6 Greatest Common Factor Practice Tests

A 10-question Grade 6 Math practice test on factors, common factors, prime factorization, greatest common factor, algorithms, and equal-group applications.

List factors or use prime factorization, identify the factors shared by the numbers, and select the greatest common factor.

10 Questions
0/10 Questions0 %
Correct 0
Incorrect 0
Unanswered 10
1. QuestionMultiple choice

What is the prime factorization of 12?

Please select an answer first.

Correct answer: A

The correct answer is 22×32^2 \times 3.

  1. List the factors: Find the positive factors of each number or use prime factorization.
  2. Identify the common factors: 12=2×2×3=22×312 = 2 \times 2 \times 3 = 2^2 \times 3.
  3. Choose the greatest one: The greatest common factor must divide both numbers and be at least as large as every other common factor.

12=2×2×3=22×312 = 2 \times 2 \times 3 = 2^2 \times 3.

2. QuestionMultiple choice

What is the prime factorization of 18?

Please select an answer first.

Correct answer: B

The correct answer is 2×322 \times 3^2.

  1. List the factors: Find the positive factors of each number or use prime factorization.
  2. Identify the common factors: 18=2×3×3=2×3218 = 2 \times 3 \times 3 = 2 \times 3^2.
  3. Choose the greatest one: The greatest common factor must divide both numbers and be at least as large as every other common factor.

18=2×3×3=2×3218 = 2 \times 3 \times 3 = 2 \times 3^2.

3. QuestionMultiple choice

What is the prime factorization of 24?

Please select an answer first.

Correct answer: C

The correct answer is 23×32^3 \times 3.

  1. List the factors: Find the positive factors of each number or use prime factorization.
  2. Identify the common factors: 24=2×2×2×3=23×324 = 2 \times 2 \times 2 \times 3 = 2^3 \times 3.
  3. Choose the greatest one: The greatest common factor must divide both numbers and be at least as large as every other common factor.

24=2×2×2×3=23×324 = 2 \times 2 \times 2 \times 3 = 2^3 \times 3.

4. QuestionMultiple choice

What is the prime factorization of 36?

Please select an answer first.

Correct answer: D

The correct answer is 22×322^2 \times 3^2.

  1. List the factors: Find the positive factors of each number or use prime factorization.
  2. Identify the common factors: 36=2×2×3×3=22×3236 = 2 \times 2 \times 3 \times 3 = 2^2 \times 3^2.
  3. Choose the greatest one: The greatest common factor must divide both numbers and be at least as large as every other common factor.

36=2×2×3×3=22×3236 = 2 \times 2 \times 3 \times 3 = 2^2 \times 3^2.

5. QuestionMultiple choice

What is the greatest common factor of 12 and 18 using prime factors?

Please select an answer first.

Correct answer: A

The correct answer is 66.

  1. List the factors: Find the positive factors of each number or use prime factorization.
  2. Identify the common factors: 12=22×312 = 2^2 \times 3 and 18=2×3218 = 2 \times 3^2. The common prime product is 2×3=62 \times 3 = 6.
  3. Choose the greatest one: The greatest common factor must divide both numbers and be at least as large as every other common factor.

12=22×312 = 2^2 \times 3 and 18=2×3218 = 2 \times 3^2. The common prime product is 2×3=62 \times 3 = 6.

6. QuestionMultiple choice

What is the greatest common factor of 20 and 28?

Please select an answer first.

Correct answer: B

The correct answer is 44.

  1. List the factors: Find the positive factors of each number or use prime factorization.
  2. Identify the common factors: 20=22×520 = 2^2 \times 5 and 28=22×728 = 2^2 \times 7. The shared greatest product is 22=42^2 = 4.
  3. Choose the greatest one: The greatest common factor must divide both numbers and be at least as large as every other common factor.

20=22×520 = 2^2 \times 5 and 28=22×728 = 2^2 \times 7. The shared greatest product is 22=42^2 = 4.

7. QuestionMultiple choice

What is the greatest common factor of 45 and 60?

Please select an answer first.

Correct answer: C

The correct answer is 1515.

  1. List the factors: Find the positive factors of each number or use prime factorization.
  2. Identify the common factors: 45=32×545 = 3^2 \times 5 and 60=22×3×560 = 2^2 \times 3 \times 5. The common greatest product is 3×5=153 \times 5 = 15.
  3. Choose the greatest one: The greatest common factor must divide both numbers and be at least as large as every other common factor.

45=32×545 = 3^2 \times 5 and 60=22×3×560 = 2^2 \times 3 \times 5. The common greatest product is 3×5=153 \times 5 = 15.

8. QuestionMultiple choice

What is the greatest common factor of 42 and 70?

Please select an answer first.

Correct answer: D

The correct answer is 1414.

  1. List the factors: Find the positive factors of each number or use prime factorization.
  2. Identify the common factors: 42=2×3×742 = 2 \times 3 \times 7 and 70=2×5×770 = 2 \times 5 \times 7. The shared product is 2×7=142 \times 7 = 14.
  3. Choose the greatest one: The greatest common factor must divide both numbers and be at least as large as every other common factor.

42=2×3×742 = 2 \times 3 \times 7 and 70=2×5×770 = 2 \times 5 \times 7. The shared product is 2×7=142 \times 7 = 14.

9. QuestionMultiple choice

What is the greatest common factor of 32 and 48?

Please select an answer first.

Correct answer: A

The correct answer is 1616.

  1. List the factors: Find the positive factors of each number or use prime factorization.
  2. Identify the common factors: 32=2532 = 2^5 and 48=24×348 = 2^4 \times 3. The smaller power gives 24=162^4 = 16.
  3. Choose the greatest one: The greatest common factor must divide both numbers and be at least as large as every other common factor.

32=2532 = 2^5 and 48=24×348 = 2^4 \times 3. The smaller power gives 24=162^4 = 16.

10. QuestionMultiple choice

What is the greatest common factor of 54 and 72?

Please select an answer first.

Correct answer: B

The correct answer is 1818.

  1. List the factors: Find the positive factors of each number or use prime factorization.
  2. Identify the common factors: 54=2×3354 = 2 \times 3^3 and 72=23×3272 = 2^3 \times 3^2. Use 2×32=182 \times 3^2 = 18.
  3. Choose the greatest one: The greatest common factor must divide both numbers and be at least as large as every other common factor.

54=2×3354 = 2 \times 3^3 and 72=23×3272 = 2^3 \times 3^2. Use 2×32=182 \times 3^2 = 18.

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Frequently asked questions about Grade 6 Greatest Common Factor

What topics are covered?

The page covers factors, factor pairs, common factors, prime factorization, the Euclidean algorithm, GCF versus LCM, fraction simplification, and equal-group applications.

When is the GCF useful?

The GCF helps simplify fractions and find the greatest number of equal groups or the greatest equal measurement that divides several quantities.

How many questions are on this page?

The page includes five mini tests with 10 questions each, for 50 Grade 6 Greatest Common Factor questions in total.