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Vocabulary

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

2. Greatest common factor- the largest factor that two or more numbers have in common.

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

4. composite numbers- #'s with more than 2 factors. (4,6,8,9,10,12,14,...)

Steps to find the GCF:

• 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.

Find the GCF of 12 and 20

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 =

What is Factoring?

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.

Simplifying an Expression by Factoring

Let's start with this expression:

12a + 24

Simplifying an Expression by Factoring

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?

Simplifying an Expression by Factoring

Simplifying an Expression by Factoring

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!