Every number can be expressed as the product of 1 or more prime numbers. When you write a number this way, you have found its prime factorization. For example:
Finding the prime factorization of a number can come in handy for doing lots of things, so make sure you know how to do so. Let's say you need to come up with the prime factorization of 108.
First of all, it's clear that 108 is an even number, so 2 is one of the factors. So, rewrite 108 as:
108 = 2*54.
Since 54 is still an even number, you can write 2 as a factor again, like so:
108 = 2*2*27
108 = 22 * 27
At this point, you might realize that 27 is 3 cubed, so:
108 = 22 * 33.
Now, the only numbers you are multiplying are 2 and 3, which are prime numbers. That's how you know you are done finding the prime factorization.
There are many ways to go about finding a prime factorization. For example, if you knew that 108 = 9 * 12, you might start by finding the prime factorizations of 9 (32) and 12 (22 * 3). Then you would determine the prime factorization of 108 as follows:
108 = 9 * 12
108 = 32 * 22 * 3
108 = 22 * 33.
No matter what, you end up with the same prime factorization for 108. That's because every number has only one prime factorization.