Factoring! Greatest Common Factor

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1. Factors- #'s multiplied together to get a product. (5x2=10, 5 and 2 are factors of 10)

3. prime numbers- #'s with exactly 2 factors. (2,3,5,7,11,13,17,...)

• Find ALL factors of each number.

• Write the factors in numerical order from least to greatest.

• Find the common factors (CF)

• The greatest of the common factors is the GCF.

Factors of 12                     Factors of 20
1 x 12                                      1 x 20            

2 x 6                                        2 x 10                        

3 x 4                                        4 x 5 

12 = 1, 2, 3, 4, 6, 12
20 = 1, 2, 4, 5, 10, 20

Common factors (CF) of 12 and 20
CF = 1, 2, 4
GCF = 4

What is the GCF of 24 and 40?

24 =

40 =​

GCF =

​

What is the GCF of 9 and 22?

9 =

22 =​

GCF =

Finding the GCF between all terms and "factoring" (dividing it out) of each term. *It is the reverse of the distributive property.

We factor expressions for a few reasons:

1. To easily identify the different variables and terms of the expression.

2. To solve for an unknown variable in fewer steps.

Let's start with this expression:

12a + 24

First, we need to identify the numbers that we will find the GCF of.

12a + 24: the numbers are 12 and 24.

Question 1: What is the GCF of 12 and 24?

Now that we have our simplified terms, we can't forget how we simplified them!

Always write the GCF in front of the terms!!!!

12(a + 2)

Question 2: Let's practice finding the GCF some more!