Download 4.5 GCF and Factoring by Finding a GCF

4.5 GCF and Factoring by Finding a GCF
GCF stands for _____________________ _____________________ _____________________ and is the
Factors of a number are
Example – List the factors of 20:
How to find the GCF:
1. List all of the factors of each number
2. Find the largest factor that both numbers have in common – that is your GCF
Examples – Find the GCF of the following:
a.) 16 and 24
b.) 12 and 36
c.) 10 and 45
d.) 16
and 28
e.) 30 and 9
f.) 21 and
What if there are variables included? Same idea – ask yourself, what is the largest amount of that variable that both terms
have in common?
Example – Find the GCF of 𝑥 4 and 𝑥 3
1.) Make a chart that shows how many variables each term represents
2.) What is the largest amount that they both have in common?
** Here’s a hint – the GCF of the variables will always be the variable with the smallest power **
Examples – Find the GCF of the variables.
g.) 𝑥 6 𝑎𝑛𝑑 𝑥 2
h.) 𝑦 𝑎𝑛𝑑 𝑦 4
j.) 𝑥 8 𝑎𝑛𝑑 𝑥 5
i.) 𝑥 5 𝑎𝑛𝑑 𝑥 6
k.) 𝑚3 𝑎𝑛𝑑 𝑚2
What if the terms have a number and a variable? We simply find the GCF of both, smush them together, and that is the
complete GCF!
Examples – Find the GCF of terms.
l.) 12𝑥 3 𝑎𝑛𝑑
16𝑥 6
m.) 9𝑦 5 𝑎𝑛𝑑 15𝑦 2
n.) 34𝑥 7 𝑎𝑛𝑑 24𝑥 5
o.) 18𝑎3 𝑎𝑛𝑑 30𝑎4
Factoring by Taking out a GCF
1. Find the GCF of the numbers
2. Find the GCF of the variables
3. Put these GCFs together to create one
term, write it outside of a set of parentheses
4. Inside of the parentheses, write what is left
Examples – Factor by taking out the GCF.
p.) 5𝑥 2 − 15𝑥
q.) 3𝑥 4 + 12𝑥 7
r.) 20𝑦 8 − 14𝑦 6
s.)
t.)
u.)
v.)
w.)
x.)