Prime Factorization
There are different methods which can be utilized to find the prime factorization of a
number. One way is to repeatedly divide by prime numbers:
EXAMPLE
1.
Prime factorization of 96 (by division):
96 ÷ 2 = 48
48 ÷ 2 = 24
24 ÷ 2 = 12
12 ÷ 2 = 6
6÷2=3
3÷3=1
96 = 2 * 2 * 2 * 2 * 2 * 3
EXAMPLE
2.
Prime factorization of 120 (by division):
120 ÷ 2 = 60
60 ÷ 2 = 30
30 ÷ 2 = 15
15 ÷ 3 = 5
5÷5=1
120 = 2 * 2 * 2 * 3 * 5
Another way to approach the task is to choose ANY pair of factors and split these factors
until all the factors are prime:
Traditionally, the factors are listed in order from least to greatest.
While the product would be the same regardless of the order of the factors, it is much
easier to compare or evaluate expressions if the factors are listed in this order.
Prime Factorization
Name: _____________________
Date: _____________________
Find the prime factorization of the following numbers: *Choose the method
you’re most comfortable with AND show all work (as in the examples on the
first page).
A) 30
B) 45
C) 150
D) 64
E) 70
F) 82
G) 24
H) 58
I) 200
J) 220