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.

---

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

Derived 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

Ashwill is a baseball historian and co-founded the Seamheads Negro Leagues Database, which Major League Baseball cited as a prime factor in its decision to incorporate Negro-leagues records.

From New York Times • Mar. 23, 2021

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

From Textbooks • Apr. 22, 2020

Concentration.—It has been said that great concentration of mind—the ability to exclude all objects and subjects except the one under consideration—is the prime factor of genius, and an adequate explanation of its achievements.

From Studies in the Out-Lying Fields of Psychic Science by Tuttle, Hudson