Prime Factorizations

Pre-Algebra Tutorial

Prime Factorizations


Given the example of two numbers multiplied, we can break down the factors of both numbers to form the product made with only prime numbers.
A prime number is a whole number that can only be divisible by itself and 1.
Some examples of the smallest prime numbers are; 1, 2, 3, 5, and 7.
Using these numbers, we can test for the prime numbers that compose a greater number.

Sample Problem

Find the prime factors of the equation 6 x 12 = 72.


The first step is to look at each factor and determine if it can be broken down further.
The easiest way to do this is to divide each factor by two, and keep dividing the whole numbers by two until they are prime; divisible only by itself and 1.

6 x 12 = 72
^ ^
2×3 2×6

Now that the prime factors have been found, we can combine all factors to equal the original solution of the equation.

2 x 2 x 2 x 3 x 3 = 72

( 2 x 3 ) x ( 2 x 2 x 3 ) = 72
(6) x (12) = 72

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