# Prime Factorization

Prime factorization (also known as finding the Product of Primes) is a skill that many people learn in middle school, but never really understand what they are doing or why.

It is important that you not only learn how to do a prime factorization, but that you understand what you are being asked to do when you hear the terms prime factorization or product of primes.

Notice that both titles have the word prime.  Also remember that the prime numbers begin with 2, 3, 5, 7, 11, 13, etc.  Factors are number that are multiplied together to get a product, so a prime factorization is a multiplication problem made up of only prime numbers to get a given product.

Here's an example:  45 can be written as 3 X 3 X 5.  Notice that 3 and 5 are both prime numbers, so 3 X 3 X 5 = 45 is writing the prime factorization of 45.

All of the factors must be prime and prime factors can be used more than once.

The prime factorization of 56 is 2 X 2 X 2 X 7.

Try coming up with the prime factorization for the number 252.  If you don't have a method for doing this you could spend a lot of time guessing and checking.

Many students learn to do prime factorization using factor trees.  Factor trees definitely work, but can get long and messy!  Here are some videos that show a different method that is much quicker and compact.

In order to understand the first prime factorization video, it is helpful to have a short lesson on a technique called short division.  Most students learn long division in school, and many people forget how to do it as adults.  This first video will give you a quick lesson on short division.

https://youtu.be/SLze82Zcc4Y

Here's  video showing a short division method for doing a prime factorization.  Pay attention to the end where the final answer is written using exponents.

https://youtu.be/EFlzv5L0sb

Here's another example showing how this method can be efficient even for a really large number.

https://youtu.be/-RhdzNYfF-M

There are a lot of videos that show both this method and factor trees if you need more examples.

Fortunately you won't be doing prime factorization for very large numbers very often, but being able to write two and three digit numbers in prime factored form can come in very handy.

Here's a worksheet for you to practice.  Remember that you can always check to see if your prime factorization is correct.  Are all of the factors prime and when you multiply the factors together, do you get back to your original number?