Prime Factorization

Pronunciation: /praɪm ˈfæk.təˌraɪ.zeɪ.ʃən/ Explain

Prime factors are a set of prime numbers that, when multiplied together, give a specific number or expression. Prime factorization is the process of finding all prime factors of a number.

A prime number is a number that is evenly divisible only by 1 and itself. A prime factor may be a number or an expression. A prime expression, just like a prime number, is only evenly divisible by 1 and itself. Examples of expressions that are prime include

  • (x + 1)
  • (3t - 2)
  • 6y

Prime factor tree
Figure 1: A prime factor tree

To find prime factors, you can use prime factorization to find common factors. The method most often used to get the prime factorization of a number is a factor tree. Figure 1 contains an example of a factor tree. If you can split each number in the tree into two or more factors, you split it. You stop when all the numbers at the bottom of the tree are prime numbers.


  1. McAdams, David E.. All Math Words Dictionary, prime factorization. 2nd Classroom edition 20150108-4799968. pg 144. Life is a Story Problem LLC. January 8, 2015. Buy the book

More Information

  • McAdams, David E.. Factor. All Math Words Encyclopedia. Life is a Story Problem LLC. 3/12/2009.

Cite this article as:

McAdams, David E. Prime Factorization. 12/21/2018. All Math Words Encyclopedia. Life is a Story Problem LLC.

Image Credits

Revision History

12/21/2018: Reviewed and corrected IPA pronunication. (McAdams, David E.)
12/1/2018: Removed broken links, updated license, implemented new markup. (McAdams, David E.)
7/12/2007: Initial version. (McAdams, David E.)

All Math Words Encyclopedia is a service of Life is a Story Problem LLC.
Copyright © 2018 Life is a Story Problem LLC. All rights reserved.
This work is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License