Factoring! Greatest Common Factor

Factoring! Greatest Common Factor

By Mr. Ginarte

Poll

Which pet is your favorite?

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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 =

Multiple Choice

What is a factor?

• a factor is when you divide two numbers to get another number

• a number that multiplies with another number to get a product

• a factor the answer to a multiplication problem

• the same as a multiple

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?

Multiple Choice

What is the GCF of 12 and 24?

• 24

• 12

• 6

• 2

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!

Multiple Choice

What is the GCF of 5 and 20?

• 2

• 5

• 4

• 20

Fill in the Blanks

What is the GCF of 16 and 36?

Multiple Choice

What is the GCF in this expression?

24x + 30

• 6

• 10

• 8

• 4

Multiple Choice

What is the GCF in this expression?

24x⁴ + 30x³

• 6x³

• 10x²

• 8x

• 4