Greatest Common Factor (GCF)

Textbook page 160

What are common factors?

Common factors are factors shared by two or more numbers.

What is the greatest common factor?

The greatest common factor (GCF) is the largest of the common factors for a set of numbers.

Example 1:Find the GCF of each set of numbers.

List the factors(A) 16 and 24

1x16 1x24 * First, list 2x8 2x12 all the 4x4 3x8 factors

4x6 * circle the

GCF

Example 1:Find the GCF of each set of numbers.

Use prime factorization(B) 12, 24, and 32

12 24 32

3 4 4 6 4 8

2 2 2 2 2 3 2 2 2 4

2 2

•Write the prime factorization of each•Find common primes•Multiply the common primes to get the GCF 2 x 2 = 4

Example 1:Find the GCF of each set of numbers.

Use a ladder diagram(A) 12, 18, and 60

2 I 12 I 18 I 60 3 I 6 I 9 I 30

2 3 10• Begin with a common factor

that divides into each.• Continue until there are no

more common factors.• Multiply the factors that were

common.2 x 3 = 6

Example 2: There are 12 boys and 18 girls in Mr. Ruiz’s science class. The students must form lab groups. Each

group must have the same number of boys and the same number of girls. What is the greatest number of groups Mr. Ruiz can make if every student must be in a group?

Step 1 –Understand the problem

We need to make groups with the same number of boys in each group and the same number of girls in each group.

Example 2: There are 12 boys and 18 girls in Mr. Ruiz’s science class. The students must form lab groups. Each

group must have the same number of boys and the same number of girls. What is the greatest number of groups Mr. Ruiz can make if every student must be in a group?

Step 2 –Make a plan

Choose how you want to solve it.

• List the factors• Use prime factorization• A ladder diagram

Example 2: There are 12 boys and 18 girls in Mr. Ruiz’s science class. The students must form lab groups. Each

group must have the same number of boys and the same number of girls. What is the greatest number of groups Mr. Ruiz can make if every student must be in a group?

Step 3 –Solve

12 181x12 1x182x6 2x93x4 3x6

6 groups: 2 boys and 3 girls in each group

Example 2: There are 12 boys and 18 girls in Mr. Ruiz’s science class. The students must form lab groups. Each

group must have the same number of boys and the same number of girls. What is the greatest number of groups Mr. Ruiz can make if every student must be in a group?

Step 4 –Look Back

Use a different method to get the answer to check your work.