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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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5. Test

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

How is the greatest common factor different from the least common multiple?

Please select an answer first.

Correct answer: A

The correct answer is The GCF is the greatest shared divisor, while the LCM is the least shared multiple..

  1. List the factors: Find the positive factors of each number or use prime factorization.
  2. Identify the common factors: A factor divides a number, while a multiple is a product of a number and a whole number.
  3. Choose the greatest one: The greatest common factor must divide both numbers and be at least as large as every other common factor.

A factor divides a number, while a multiple is a product of a number and a whole number.

2. QuestionMultiple choice

If the greatest common factor of two numbers is 6, which statement must be true?

Please select an answer first.

Correct answer: B

The correct answer is 6 divides both numbers..

  1. List the factors: Find the positive factors of each number or use prime factorization.
  2. Identify the common factors: By definition, a common factor divides both numbers, and the greatest common factor is one such divisor.
  3. Choose the greatest one: The greatest common factor must divide both numbers and be at least as large as every other common factor.

By definition, a common factor divides both numbers, and the greatest common factor is one such divisor.

3. QuestionMultiple choice

When using the Euclidean algorithm for 84 and 30, what is the first remainder?

Please select an answer first.

Correct answer: C

The correct answer is 2424.

  1. List the factors: Find the positive factors of each number or use prime factorization.
  2. Identify the common factors: 84=30×2+2484 = 30 \times 2 + 24, so the first remainder is 24.
  3. Choose the greatest one: The greatest common factor must divide both numbers and be at least as large as every other common factor.

84=30×2+2484 = 30 \times 2 + 24, so the first remainder is 24.

4. QuestionMultiple choice

If one positive number divides another exactly, what is their greatest common factor?

Please select an answer first.

Correct answer: D

The correct answer is The smaller number.

  1. List the factors: Find the positive factors of each number or use prime factorization.
  2. Identify the common factors: If the smaller number divides the larger, it is a common factor and no factor of the smaller can be greater than it.
  3. Choose the greatest one: The greatest common factor must divide both numbers and be at least as large as every other common factor.

If the smaller number divides the larger, it is a common factor and no factor of the smaller can be greater than it.

5. QuestionMultiple choice

What is the greatest common factor of 24 and 40?

Please select an answer first.

Correct answer: A

The correct answer is 88.

  1. List the factors: Find the positive factors of each number or use prime factorization.
  2. Identify the common factors: 24=8×324 = 8 \times 3 and 40=8×540 = 8 \times 5, so the greatest common factor is 8.
  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=8×324 = 8 \times 3 and 40=8×540 = 8 \times 5, so the greatest common factor is 8.

6. QuestionMultiple choice

What is GCF(18,30)GCF(18,30)?

Please select an answer first.

Correct answer: B

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: The common factors are 1, 2, 3, and 6; the greatest is 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.

The common factors are 1, 2, 3, and 6; the greatest is 6.

7. QuestionMultiple choice

What is a common error when finding a greatest common factor?

Please select an answer first.

Correct answer: C

The correct answer is Choosing a common multiple instead of a common factor..

  1. List the factors: Find the positive factors of each number or use prime factorization.
  2. Identify the common factors: A GCF must divide both numbers. A large product that is a multiple of both numbers is not a factor.
  3. Choose the greatest one: The greatest common factor must divide both numbers and be at least as large as every other common factor.

A GCF must divide both numbers. A large product that is a multiple of both numbers is not a factor.

8. QuestionMultiple choice

What is the greatest common factor of 49 and 77?

Please select an answer first.

Correct answer: D

The correct answer is 77.

  1. List the factors: Find the positive factors of each number or use prime factorization.
  2. Identify the common factors: 49=7×749 = 7 \times 7 and 77=7×1177 = 7 \times 11, so the greatest shared factor is 7.
  3. Choose the greatest one: The greatest common factor must divide both numbers and be at least as large as every other common factor.

49=7×749 = 7 \times 7 and 77=7×1177 = 7 \times 11, so the greatest shared factor is 7.

9. QuestionMultiple choice

How can you verify a proposed greatest common factor?

Please select an answer first.

Correct answer: A

The correct answer is Check that it divides both numbers and that no larger common factor exists..

  1. List the factors: Find the positive factors of each number or use prime factorization.
  2. Identify the common factors: A valid GCF must be a common divisor and must be greater than or equal to every other common factor.
  3. Choose the greatest one: The greatest common factor must divide both numbers and be at least as large as every other common factor.

A valid GCF must be a common divisor and must be greater than or equal to every other common factor.

10. QuestionMultiple choice

Which summary best describes Grade 6 Greatest Common Factor?

Please select an answer first.

Correct answer: B

The correct answer is The GCF is the greatest positive factor shared by two or more numbers and helps simplify fractions and create equal groups..

  1. List the factors: Find the positive factors of each number or use prime factorization.
  2. Identify the common factors: A complete summary connects factors, prime factorization, algorithms, simplification, and equal-group applications.
  3. Choose the greatest one: The greatest common factor must divide both numbers and be at least as large as every other common factor.

A complete summary connects factors, prime factorization, algorithms, simplification, and equal-group applications.

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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.