Prime Factorization

Pronunciation: /praɪm ˈfæk təˌraɪ zeɪ ʃən/ ?

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.

More Information

  • McAdams, David. Factor. allmathwords.org. All Math Words Encyclopedia. Life is a Story Problem LLC. 2009-03-12. http://www.allmathwords.org/article.aspx?lang=en&id=Factor.
  • McAdams, David. Greatest Common Factor. allmathwords.org. All Math Words Encyclopedia. Life is a Story Problem LLC. 2009-03-12. http://www.allmathwords.org/article.aspx?lang=en&id=Greatest%20Common%20Factor.
  • McAdams, David. Common Factor. allmathwords.org. All Math Words Encyclopedia. Life is a Story Problem LLC. 2009-03-12. http://www.allmathwords.org/article.aspx?lang=en&id=Common%20Factor.
  • How to Use Prime Factorization on Composite Numbers (video). dummies.com. Wiley. 2010-01-23. http://www.dummies.com/how-to/content/how-to-use-prime-factorization-on-composite-numbers.html.

Cite this article as:


Prime Factorization. 2007-07-12. All Math Words Encyclopedia. Life is a Story Problem LLC. http://www.allmathwords.org/en/p/primefactorization.html.

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2007-07-12: Initial version (McAdams, David.)

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