1. Greatest Common Factor

2. Greatest Common Factor
The greatest common factor (GCF) is the product of the prime factors both numbers have in common. Or
It is the largest number that is a factor of all original numbers.

3. Find the Greatest Common Factor
Example: 18xy , 36y2
18xy = 2 · 3 · 3 · x · y
36y2 = 2 · 2 · 3 · 3 · y · y
GCF = 2
· 3
· 3
· y
= 18y

4. Tips for finding the GCF
Find the prime factorization of each item.
Circle what is common.
Multiply together what is common to get the GCF.

5. Now you try! Find the greatest common factor of the following:
Example 1: 12a2b , 90a2b2c
GCF = 6a2b
Example 2: 15r2 , 35s2 , 70rs
GCF = 5

6. Last Example
What is the greatest common factor of 15ab and 16c?

7. Factoring Using the GCF

8. Factoring
“Undoing” distribution
Finding factors that, when multiplied, form the original polynomial

9. Example: Factor: 12a2 + 16a = 2·2·3·a·a + 2·2·2·2·a = 2 · 2 · a
1. Factor each term.
= 2·2·3·a·a + 2·2·2·2·a
2. Factor out the GCF.
= 2
· 2
· a
(3·a + 2·2)
= 4a (3a + 4)
3. Multiply.
You can check by distributing.

10. Example:
Factor: 18cd2 + 12c2d + 9cd
= 2·3·3·c·d·d + 2·2·3·c·c·d + 3·3·c·d
= 3
· c
· d
(2·3·d + 2·2·c + 3)
= 3cd (6d + 4c + 3)

11. Now you try! Example 1: 15x + 25x2 Example 2: 12xy + 24xy2 – 30x2y4
= 6xy(2 + 4y – 5xy3)

12. One last example: Factor: 4x + 12x2 + 16x3
= 2·2·x· + 2·2·3·x·x + 2·2·2·2·x·x·x
= 2
· 2
· x
(1 + 3·x + 2·2·x·x)
= 4x (1 + 3x + 4x2)