3.2 Factoring Linear Expression
GCF
• Also known as:
The Greatest Common Factor
• Also known as:
The largest number that can be divided into all
Finding the Greatest Common Factor
Cake Method
For example,
Find the GCF of 28 and 36
Hmm….
Hmm….
What
Hmm….
number
What number
What
can divide
number
can divide
both
can divide
28 and
both 14 and
both 36?
7 and 9?
18?
2
Multiply all of the
side numbers to
find the GCF
28
36
2 14
1 7
18
9
The GCF is 4.
Finding the Greatest Common Factor
Now let’s apply variables!
For example,
Find the GCF of 6ab and 4a
2
Multiply all of the
side numbers and
variables to find
the GCF
6ab
4a
a 3ab
1 3b
2a
2
The GCF is 2a.
Finding the Greatest Common Factor
Let’s kick it up a notch!
For example,
Find the GCF of 3x2y and 4xy2
x
3x2y
4xy2
3x2y
3•x•x•y
y 3xy
1 3x
4y2
4y
4y2
4•y•y
The GCF is xy.
Examples
A) Find the GCF of 14c2 and 35c
7
14c2
2
2c
c
1 2c
35c
5c
5
The GCF is 7c.
2c2
2•c•c
Examples
B) Find the GCF of 6a3b and 4a2b
2
6a3b
3b
3a
a
a 3a2b
b 3ab
1 3a
4a2b
3a3b
3•a•a•a•b
2a2b
2ab
2b
2
2a2b
2•a•a•b
2• a • a • b
The GCF is 2a2b.
Once you get the hang
of this method, you can
start to factor out more
than 1 variable, like a2
or a2b.
Homework
• Page worksheet