How to Prime Factorize

Example 1

Take 45, for example. It's not prime, where it's only factors are itself and 1. It's composite.

To prime factorize 45, think about what multiplies 45.

9 and 5.

Now, simplify those.

5 is prime, but 9 is 3 x 3. You can make a factor tree.

45

^

5 x 9

      ^

       3 x 3

45 = 5 x 3 x 3



Example 2 

How about 26/56?

Ooh, fractions.

There are actually two ways to do this problem.

You can divide down, or prime factorize.

Let's prime factorize. Find and simplify factors of 26, and do the same to 56.

26 = 2 x 13          
56    7 x 2 x 2 x 2

Now, cross out numbers in common. There is a two on the top, and a two on the bottom, so cross it out.


26 = 2 x 13          
56    7 x 2 x 2 x 2

Now you are left with a 13 on the top, and a 7 and a 4 on the bottom.

You have:

13

28

Party 'cuz you're DONE!