Finding the Greatest Common Factor (GFC)

After studying this lesson, you will be able to:

• Factor out GCFs.

Steps of Factoring:

1. Factor out the GCF

2. Look at the number of terms:

• 2 Terms: Look for the Difference of 2 Squares
• 3 Terms: Factor the Trinomial
• 4 Terms: Factor by Grouping

3. Factor Completely

4. Check by Multiplying

This lesson will concentrate on the first step of factoring: Factoring out the GCF.

Example 1

Factor 10y ² + 15y

We look for the GCF...it will be 5y

Here's how we factor: write the GCF 5y and then put parentheses: 5y

Factoring is the same as dividing, so we divide each term by 5y and we put the result in the parentheses.

10y ² divided by 5y is 2y and 15y divided by 5y is 3: 5y ( 2y + 3 ) this is the answer

We can check the answer by multiplying 5y ( 2y + 3)

Distributing we will get 10y ² + 15y (which matches the original problem)

Example 2

Factor 21ab ² - 33 a ² bc

We look for the GCF......it will be 3ab

Here's how we factor: write the GCF 3ab and then put parentheses: 3ab

Factoring is the same as dividing, so we divide each term by 3ab and we put the result in the parentheses.

21ab ² divided by 3ab is 7b and - 33 a ² bc divided by 3ab is -11ac: 3ab ( 7b - 11ac ) this is the answer

We can check the answer by multiplying : 3ab ( 7b - 11ac )

Distributing we will get 21ab ² - 33 a ² bc (which matches the original problem)

Example 3

Factor 6x ³ y ² + 14x ² y + 2x ²

We look for the GCF......it will be 2x ²

Here's how we factor: write the GCF 2x ² and then put parentheses: 2x ²

Factoring is the same as dividing, so we divide each term by 2x ² and we put the result in the parentheses.

6x ³ y ² divided by 2x ² is 3xy ² and 14x ² y divided by 2x ² is 7y and 2x ² divided by 2x ² is 1

2x ²(3xy ² + 7 y + 1) this is the answer

We can check the answer by multiplying : 2x ²(3xy ² + 7 y + 1)

Distributing we will get 6x ³ y ² + 14x ² y + 2x ² (which matches the original problem)