1. Greatest Common Factor (GCF)
Textbook page 160

2. What are common factors?
Common factors are factors shared by two or more numbers.

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

4. Example 1: Find the GCF of each set of numbers.
List the factors
16 and 24
1x16 1x * First, list
2x8 2x all the
4x4 3x factors
4x * circle the
GCF

5. Example 1: Find the GCF of each set of numbers.
Use prime factorization
(B) 12, 24, and 32
2 2
Write the prime factorization of each
Find common primes
Multiply the common primes to get the GCF 2 x 2 = 4

6. Example 1: Find the GCF of each set of numbers.
Use a ladder diagram
12, 18, and 60
2 I 12 I 18 I 60
3 I I I 30
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

7. Step 1 – Understand the problem
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.

8. Choose how you want to solve it. List the factors
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

9. Example 2: There are 12 boys and 18 girls in Mr. Ruiz’s science class
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
x12 1x18 2x6 2x9 3x4 3x6 6 groups: 2 boys and 3 girls in each group

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