R4 · Lesson 3: Greatest Common Factor (GCF)

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Why this matters for Grade 6: 6.NS.4 requires using the GCF to apply the distributive property — for example, writing 12 + 18 as 6(2 + 3). You cannot do that step without finding GCF(12, 18) = 6 first. GCF is also used to simplify fractions in 6.NS.1.

Learn It

Finding the GCF

The Greatest Common Factor (GCF) of two numbers is the largest factor that both numbers share.

Method 1 — List the factors of each number, then find the largest match:

Example 1 — GCF(12, 18):

Factors of 12: 1, 2, 3, 4, 6, 12

Factors of 18: 1, 2, 3, 6, 9, 18

Common factors: 1, 2, 3, 6 — the greatest is 6.

GCF(12, 18) = 6

Example 2 — GCF(8, 12):

Factors of 8: 1, 2, 4, 8

Factors of 12: 1, 2, 3, 4, 6, 12

Common factors: 1, 2, 4 — the greatest is 4.

GCF(8, 12) = 4

Word problem connection: The GCF answers "what is the largest equal-group size with none left over?"

Example 3 — Word problem:
A teacher has 12 pencils and 18 crayons. She wants to make identical supply bags with no items left over, giving each bag the same number of pencils and the same number of crayons. What is the greatest number of bags she can make?

Answer: GCF(12, 18) = 6 bags. Each bag gets 12÷6 = 2 pencils and 18÷6 = 3 crayons.

Try It · Guided

Work These Together

1. What is GCF(12, 18)?

Hint

Factors of 12: 1, 2, 3, 4, 6, 12. Factors of 18: 1, 2, 3, 6, 9, 18. The largest number on both lists is 6.

2. What is GCF(15, 25)?

Hint

Factors of 15: 1, 3, 5, 15. Factors of 25: 1, 5, 25. Common factors: 1, 5. Greatest is 5.

Practice · On Your Own

You Try

3. What is GCF(8, 12)?

Hint

Factors of 8: 1, 2, 4, 8. Factors of 12: 1, 2, 3, 4, 6, 12. Common factors: 1, 2, 4. Greatest is 4.

4. A student has 24 red counters and 36 blue counters. What is the greatest number of equal groups she can make with no counters left over?

Hint

Find GCF(24, 36). Factors of 24: 1,2,3,4,6,8,12,24. Factors of 36: 1,2,3,4,6,9,12,18,36. The greatest common factor is 12.

5. Which of these is NOT a common factor of 12 and 18?

Hint

Factors of 18: 1, 2, 3, 6, 9, 18. Is 4 in that list? No — 18 ÷ 4 = 4.5, so 4 is NOT a factor of 18.

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Exit Ticket

Show What You Know

6. What is GCF(10, 15)?

Hint

Factors of 10: 1, 2, 5, 10. Factors of 15: 1, 3, 5, 15. The greatest common factor is 5.

7. A baker has 18 muffins and 24 cookies. She puts them into the largest possible equal groups with no items left over. How many items are in each group?

Hint

Find GCF(18, 24). Factors of 18: 1, 2, 3, 6, 9, 18. Factors of 24: 1, 2, 3, 4, 6, 8, 12, 24. GCF = 6. The baker can make 6 equal groups, each containing 18÷6 = 3 muffins and 24÷6 = 4 cookies (6 items per group).

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