How is prime factorization done?

How to Do Prime Factorization

Here is one way to do prime factorization:

We'll find the prime factorization of 98.

Though you can start with any of the factors which when multiplied together equal 98, let's start with the lowest prime factor, which is 2.

2 X 49 = 98 Now, find the lowest prime factor of 49, which is 7. 7 X 7 = 49.

Write it like this:

2 X 7 X 7 = 98, which is the prime factorization because all the factors are prime.

Here is another example:

We'll do the number 100:

2 X 50 = 100

2 X 2 X 25 (We just factored the number 50, using the lowest Prime number that will divide evenly into 50) Now, we'll factor 25. 5 X 5 = 25. Write it like this:

2 X 2 X 5 X 5

All the factors are prime now, so the prime factorization of 100 is 2 X 2 X 5 X 5.

So, basically, prime factorization is simply finding the prime factors (those which have only 1 and itself as factors) that when multiplied together equal the given number. The above examples show one way to accomplish that.