coprime

English

Alternative forms

• co-prime

Etymology

co-+‎prime

Adjective

coprime(notcomparable)

1. (number theory,of two or more positive integers)Havingnopositive integerfactorsin common,aside from1.

   24 and 35 arecoprime.

2. (number theory,of a positive integer)Having no positive integer factors, aside from 1, in common with one or more specified other positive integers.

   24 iscoprimeto 35.

3. (algebra,by extension,of two or more polynomials)Whosegreatest common divisoris a nonzero constant (i.e., polynomial of degree 0).
4. (ring theory,by extension)(of two or moreidealsof aring)Whosesumis the whole ring;(of two or moreelementsof aring)generatingthe whole ring.

Usage notes

In mathematics, this adjective can be used in phrases like "A and B are coprime", "A is coprime to B", and, less commonly, "A is coprime with B".

Synonyms

• (having no factors in common):relatively prime
• (having no factors in common with):relatively prime

Related terms

• coprimality
• coprimeness

Translations

(of two or more positive integers) having no factors in common

• Bulgarian:взаимно простиpl(vzaimno prosti)
• Chinese:

  Cantonese:Hỗ tố(wu⁶sou³)

  Mandarin:Hỗ chất／Hỗ chất(zh)(hùzhì, hùzhí),Hỗ tố(zh)(hùsù)

• Czech:nesoudělný
• Finnish:keskenäänjaottomiapl
• French:premiers entre eux(fr)
• German:teilerfremd(de),relativ prim
• Hebrew:זר(he)(zar)
• Hungarian:relatív prímek(hu)pl
• Icelandic:ósamþáttam,ósamþætturm
• Indonesian:relatif prima
• Japanese:Hỗ いに tố(ja)(tagai ni so)
• Korean:서로소(seoroso)
• Polish:względnie pierwszepl
• Portuguese:coprimo
• Russian:взаи́мно просто́й(vzaímno prostój),взаи́мно просты́еpl(vzaímno prostýje)
• Swedish:relativt prima
• Turkish:aralarında asal

(of a positive integer) having no factor in common with...

• Finnish:keskenäänjaoton...kanssa
• German:teilerfremd(de),relativ prim
• Hebrew:זר(he)(zár)
• Hungarian:relatív prím(hu)
• Polish:względnie pierwszaf
• Portuguese:coprimo

See also

• greatest common divisor

Anagrams

• meropic