prime factor

American  

[prahym fak-ter] / ˈpraɪm ˈfæk tər /

noun

1. a prime number that is a factor of another number.

   The prime factors of 18 are 2 and 3.

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verb (used with or without object)

1. Sometimes prime-factor to resolve (a number) into the prime numbers that are its factors.

   This short video shows how to prime factor a number using a tree diagram.

adjective

1. Sometimes prime-factor relating to or involving prime factors.

   Write out the prime factor expansion for each of the following numbers.

Other Word Forms

• prime factorize
  verb
• prime-factorize
  verb

Etymology

Origin of prime factor

First recorded in 1725–35

Example Sentences

The death of Franklin’s young son, Frances, from smallpox was a prime factor in his ardent support of inoculation.

From The Wall Street Journal • Apr. 14, 2026

The high cost of living is a prime factor in the ongoing exodus of many Californians, and also may help explain the relatively lackluster mood of people in the state.

From Los Angeles Times • Jan. 11, 2024

“That is the prime factor why it is growing faster and is more resilient than any other luxury — because it’s visceral, deep in our minds and hearts, and global.”

From New York Times • Nov. 21, 2022

By matching up the common primes, each common prime factor is used only once.

From Textbooks • Apr. 22, 2020

A prime factor to this end was to avoid any conflict of interests among the participants.

From The Story of the Great War, Volume VII (of VIII) American Food and Ships; Palestine; Italy invaded; Great German Offensive; Americans in Picardy; Americans on the Marne; Foch's Counteroffensive. by Various