Word.ws English Dictionary

prime factor

prime factor noun: a factor of a given integer which is also a prime number.

Noun

prime factor (plural prime factors)

  1. A factor of a given integer which is also a prime number.
    • Hence, the prime factors of 100 are 1, 2, 2, 5, 5, and 1 × 2 × 2 × 5 × 5 = 100. From the above illustration, we derive the following rule for finding all the prime factors of any composite number.1847, James Robinson, The American Arithmetic, John P. Jewett & Co., page 91
    • Theorem 5.5 Dickman's Theorem. The probability of a number N chosen at random having a prime factor between N#92;alpha and N#123;#92;alpha(1#43;#92;delta)#125; is approximately #61;#92;delta, independent of the magnitude of #92;alpha, if #92;delta is small.1994, Hans Riesel, Prime Numbers and Computer Methods for Factorization, Springer, page 161
  2. Used other than figuratively or idiomatically: see prime, factor.
    • It became apparent to me that Mr. Genthner's open profession of being gay was the prime factor in his conviction and sentencing.1989 February 12, anonymous author, “Innocent Man In Prison Because He Is Gay”, in Gay Community News, volume 16, number 30, page 5

Verb

prime factor (third-person singular simple present prime factors, present participle prime factoring, simple past and past participle prime factored)

  1. (transitive) To reduce an integer to its set of prime factors.
    • Any composite number can be prime factored; that is, it can be written as a product of prime numbers (excluding 1) in one and only one way.[…]When prime factoring numbers, it is standard to rearrange the factors so that the numbers are in increasing order.2004, Fred N. Grayson, CliffsTestPrep Military Flight Aptitude Tests, Wiley, page 39
    • For example, the number 30, which is not prime, can be prime factored as 2 x 3 x 5.2008, Phil Pine, Peterson's Master the SAT 2009, page 322

prime factor meaning in Tamil, Malay, Indonesian and Vietnamese

prime factor in Tamil

பகாக்காரணி, பகாச்சினை

prime factor in Malay

factor
faktor perdana

prime factor in Indonesian

factor
faktor prima

prime factor in Vietnamese

Translations
thừa số nguyên tố

Forms of prime factor

Noun
pluralprime factors
Verb
third-person singular presentprime factors
present participleprime factoring
past participleprime factored
pastprime factored

Questions about prime factor

What does prime factor mean?
Prime factor means a factor of a given integer which is also a prime number.
What is prime factor in Tamil?
Prime factor in Tamil is பகாக்காரணி, பகாச்சினை. See Prime factor meaning in Tamil.
What part of speech is prime factor?
Prime factor can be a noun or a verb.
What is the plural of prime factor?
The plural of prime factor is prime factors.

Words near prime factor in the dictionary

  1. prime decomposition
  2. prime decompositions
  3. prime directive
  4. prime directives
  5. prime donne
  6. prime factor
  7. prime factored
  8. prime factoring
  9. prime factorisation
  10. prime factorisations
  11. prime factorization

Source and license

Adapted from Wiktionary: prime factor (page history and authors); prime factor (Tamil Wiktionary) (page history and authors). Text available under the Creative Commons Attribution-ShareAlike 4.0 license. Word.ws reformatted the entry and added links. Wiktionary data of 2026-09-02.

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Cite this entry: “prime factor.” Word.ws, https://word.ws/prime_factor. Based on Wiktionary, CC BY-SA 4.0.