.
Finding the Greatest Common Factor
Let’s review the Cake Method
For example,
Find the GCF of 28 and 36
Hmm….
Hmm….
Hmm….
What
What
number
Whatcan
number can
divide
numberboth
can
divide both
divide
28 andboth
36?
14 and 18?
7 and 9?
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
4a2b
2b
3b
2a
3a
a
a 3a2b 2ab
b 3ab
2b
1 3a
2
2• a • a • b
The GCF is 2a2b.
3a3b
3•a•a•a•b
2a2b
2•a•a•b
Once you get the
hang of this method,
you can start to factor
out more than 1
variable, like a2 or a2b.
Try 3 numbers: 36, 60,96
Relatively Prime
• Numbers whose GFC is 1
Example:
-8, 15
-64, 81
Homework
Page 227 (15-46 even)