Lesson 4-4 Pages 164-168

Greatest Common Factor (GCF)

What you will learn!1. How to find the GCF of two

or more numbers or monomials.

2. How to use the distributive property to factor algebraic expressions.

Greatest common factorGreatest common factor

What you really need to know!

The greatest number that is a factor of two or more numbers is the greatest common factor (GCF).

What you really need to know!

In algebra, greatest common factors are used to factor expressions.

What you really need to know!

There are two main methods for finding the GCF.

Example 1: Method 1

Find the GCF of 16 and 24.

1616 2424

1 x 161 x 16 1 x 241 x 24

2 x 82 x 8 2 x 122 x 12

4 x 44 x 4 3 x 83 x 8

4 x 64 x 6

Common Common FactorsFactors

11

22

44

88

GCFGCF

88

Example 1: Method 2

Find the GCF of 16 and 24.

16 =16 = 2 x 2 x 2 x 22 x 2 x 2 x 224 =24 = 2 x 2 x 2 x 32 x 2 x 2 x 3

2 x 2 x 2 = 2 x 2 x 2 = 8 8 GCFGCF

Example 2:

Find the GCF of 28 and 35.

28 =28 = 2 x 2 x 72 x 2 x 735 =35 = 5 x 75 x 7

77

Example 3:

Find the GCF of 12, 48 and 72.

12 =12 = 2 x 2 x 2 x 2 x 33

48 =48 = 2 x 2 x 2 x 2 x 32 x 2 x 2 x 2 x 3

72 =72 = 2 x 2 x 2 x 3 x 32 x 2 x 2 x 3 x 3

2 x 2 x 3 = 12 GCF

Example 4:

Parents donated 150 chocolate chip cookies and 120 molasses cookies for a school bake sale.

Example 4:

If the cookies are arranged on plates, and each plate has the same number of chocolate chip cookies and each plate has the same number of molasses cookies, what is the largest number of plates possible?

120 =120 = 2 x 2 x 2 x 3 x 52 x 2 x 2 x 3 x 5

150 =150 = 2 x 3 x 5 x 52 x 3 x 5 x 5

2 x 3 x 5 = 30 GCF

30 plates

Example 4:

How many chocolate chip and molasses cookies will be on each plate?

150 150 ÷ 30 = ÷ 30 = 5 Chocolate chip5 Chocolate chip120 120 ÷ 30 = ÷ 30 = 4 Molasses4 Molasses

Example 5:

18x18x33yy2 2 == 2 2 • 3 • 3 • x • x • x • y • y• 3 • 3 • x • x • x • y • y

42xy42xy2 2 == 2 2 • 3 • 7 • x • y • y• 3 • 7 • x • y • y

2 2 • 3 • x • y • y = 6xy• 3 • x • y • y = 6xy22

Find the GCF:

Example 6:

Factor: 3x + 12Since 3 and 12 are both divisible by 3, you can use the distributive property to rewrite the expression as 3(x + 4)

Page 167

Guided Practice

#’s 4-16

Pages 164-166 with someone at home and study

examples!

Read:

Homework: Pages 167-168

#’s 18-54 even

#’s 59-60, 67-81

Lesson Check 4-4

Page

731

Lesson 4-4

Lesson Check 4-4

Prepare for Mid-Test!

Pages 191-193

#’s 9-39Odd Answers in Back of Book!