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

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

From Textbooks • Apr. 22, 2020

His firm's survey data show that 87 percent of consumers say price will be the prime factor in deciding what to buy this holiday, up 3 percentage points from last year.

From Reuters • Oct. 5, 2015

The Duke of Buckingham now appears upon the scene as the prime factor in the events that followed.

From The Strife of the Roses and Days of the Tudors in the West by Rogers, William Henry Hamilton