Grade 6 Math · Topic 34

Greatest Common Factor (GCF)

The greatest common factor (GCF) of two numbers is the largest whole number that divides both of them evenly. The GCF is super useful for simplifying fractions and factoring expressions.

Lesson alignment: 6.NS.B.4 · Take your time. You can return to this lesson whenever you need it.

Explore visually

Find the greatest common factor

Compare the factors of two numbers. The largest shared factor is their GCF.

Think first: Which factors do you predict both numbers share, and which shared factor is greatest?

Ready? Reveal the model and try your prediction

Swipe horizontally to see the full diagram.

Turn on JavaScript to adjust this model. The examples and practice below work without it.

Follow the worked examples

Read each step, then cover the explanation and see if you can explain why it works.

Worked example 1

Find the GCF of 24 and 36.

Prime factorize: 24 = 2³ × 3, 36 = 2² × 3². Shared primes: 2 (smaller exp 2) and 3 (smaller exp 1). GCF = 2² × 3 = 12.

Answer: 12

Worked example 2

Find the GCF of 45 and 60.

Start by writing the calculation clearly: 45 = 3² × 5, 60 = 2² × 3 × 5. Shared: 3¹ and 5¹. GCF = 3 × 5 = 15.

Answer: 15

Try a few on your own

Work these on paper first. Open “Check” when you are ready to compare your answer.

  1. GCF(8, 12) =
    Check

    4

  2. GCF(15, 25) =
    Check

    5

  3. GCF(18, 27) =
    Check

    9

  4. GCF(20, 30) =
    Check

    10

  5. GCF(36, 48) =
    Check

    12

  6. GCF(50, 75) =
    Check

    25

  7. GCF(42, 70) =
    Check

    14

  8. GCF(72, 108) =
    Check

    36

Try this situation 1

Maya has 24 red beads and 36 blue beads. She wants to make identical bracelets with the same mix on each. What is the greatest number of bracelets she can make?

Show a worked solution

Answer: 12 bracelets.

She needs the GCF of 24 and 36, which is 12. Each bracelet gets 2 red and 3 blue beads.

Try this situation 2

Two ribbons are 45 in and 60 in long. They will be cut into equal pieces with no leftovers. What is the longest each piece can be?

Show a worked solution

Answer: 15 inches.

Longest equal piece = GCF(45, 60) = 15.

Fresh questions · saved on this device

Practice this skill

18 question pool

Try a fresh set each time. Answer one question, check your thinking, and read the explanation. If you miss one, return to the visual model and try another round.

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Check what you learned

Answer these five questions on your own. You can review the explanations after you submit and try again whenever you like. This short check is for practice, not a grade.

1. What is the greatest common factor (GCF) of 36 and 60?

2. What is the greatest common factor (GCF) of 24 and 36?

3. What is the greatest common factor of 36 and 54?

4. What is the greatest common factor of 42 and 63?

5. Find the greatest common factor (GCF) of 18 and 30.

Practice and finish

Try the linked topic quiz for more practice. If something is tricky, return to the example and look for the step that changes the numbers or representation.

Open the practice quiz

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More Grade 6 resources

Use these free materials if you want another explanation, extra paper practice, or a broader review.

Browse free Grade 6 topic lessons ↗Print Grade 6 worksheets ↗Review Grade 6 flashcards ↗Open the formula review ↗Try the Factors, Multiples & Percents quiz ↗Try a full practice test ↗