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 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.
16
24
1 x 16 1 x 24
2 x 8 2 x 12
4x4 3x8
4x6
Common
Factors
1
2
4
8
GCF
8
Example 1: Method 2
Find the GCF of 16 and 24.
16 = 2 x 2 x 2 x 2
24 = 2 x 2 x 2
x3
2x2x2=
8 GCF
Example 2:
Find the GCF of 28 and 35.
28 = 2 x 2
x7
35 =
5x7
7
Example 3:
Find the GCF of 12, 48 and 72.
12 = 2 x 2 x
3
48 = 2 x 2 x 2 x 2 x 3
72 = 2 x 2 x 2 x
3x3
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 = 2 x 2 x 2 x 3 x 5
150 = 2 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 ÷ 30 = 5 Chocolate chip
120 ÷ 30 = 4 Molasses
Example 5:
Find the GCF:
2•3•3•x•x•x•y•y
2
42xy = 2 • 3 • 7 • x • y • y
3
2
18x y =
2•3•x•y•y=
2
6xy
Example 6:
Factor: 3x + 12
Since 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
Read:
Pages 164-166
with someone at
home and study
examples!
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 9-39
Odd Answers in Back of Book!