Prime Factorization

Pre-Algebra Tutorial

Prime Factorization

Intro

Prime factorization is factoring out a number of its prime factors. A primary number is a number times by 1 and itself. A composite number has more than two factors. 1 can not be a prime factor since it only has one factor, which is only 1.
For example:
12=2*2*3
28=2*2*7
18=2*3*3

Sample Problem

What is the prime factorization of 144?

Solution

1. List all the factors of 144.
1,2,3,4,6,8,9,12,16,18,24,36,48,72, and 144

2. Remember, find only the prime factors.
2 and 3

3. Use that prime factor(s) to multiply to get to 144.
2*2*2*2*3*3=144.

Optional: if you want to take it a step further, you can use exponents.
Remember to use orders of operations or known as PEMDAS.
Remember that multiplication, division and addition and subtraction are read left to right.
2^4*3^2=144
16*3^2=144
16*9=144
144=144



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