Dictionary

greatest common divisor en · NOUN

Pronunciation

• /ˈɡɹeɪ.tɪst ˈkɒm.ən dɪˈvaɪ.zə/ (Received-Pronunciation)
• /ˈɡɹeɪ.tɪst ˈkɑ.mɪn dɪˈvaɪ.zɚ/ (General-American)
• (UK) audio

Meanings

1. The largest positive integer (respectively polynomial, element of a given ring) that is a divisor of each of a given set of integers (respectively polynomials, elements of a given ring).
   • 1974, John M. Peterson, Basic Concepts of Elementary Mathematics, Prindle, Weber & Schmidt, page 148, Euclid's algorithm is a process for finding the greatest common divisor of any two whole numbers.
   • Suppose (a#95;0,a#95;1,#92;dots,a#95;n)#92;in#92;Z we say (a#95;0,a#95;1,#92;dots,a#95;n) is primitive if the greatest common divisor of a#95;0,a#95;1,#92;dots,a#95;n is 1. 2006, W. B. Vasantha Kandasamy, Florentin Smarandache, Neutrosophic Rings, Hexis, page 53:
   • This paper presents a regularization theory for numerical computation of polynomial greatest common divisors and a convergence analysis, along with a detailed description of a blackbox-type algorithm.[…]As one of the fundamental algebraic problems with a long history, finding the greatest common divisor (GCD) of univariate polynomials is an indispensable component of many algebraic computations besides being an important problem in its own right. 2011, Zhonggang Zeng, “The Numerical Greatest Common Divisor of Univariate Polynomials”, in Leonid Gurvits, Philippe Pébay, J. Maurice Rojas, David Thompson, editors, Randomization, Relaxation, and Complexity in Polynomial Equation Solving, American Mathematical Society, page 187:
   • The greatest common divisor of 66, 30 and 18 is 6.

Forms

Antonyms

least common multiple (antonym(s) of “largest number that divides each of a set of positive integers”)

Relateds

maximal common divisor

Synonyms

greatest common factor (largest number that divides each of a set of positive integers) · highest common factor (largest number that divides each of a set of positive integers) · greatest common denominator (largest number that divides each of a set of positive integers) · gcd (largest number that divides each of a set of positive integers)

Translations (44)

th ตัวหารร่วมมาก (largest positive integer or polynomial) · ro cel mai mare divizor comun (largest positive integer or polynomial) · ja 最大公約数 (largest positive integer or polynomial) · az ən böyük ortaq bölən (largest positive integer or polynomial) · no største felles nevner (largest positive integer or polynomial) · pt máximo divisor comum (largest positive integer or polynomial) · is stærsti sameiginlegi deilir (largest positive integer or polynomial) · ro c.m.m.d.c (largest positive integer or polynomial) · fi suurin yhteinen tekijä (largest positive integer or polynomial) · tr en büyük ortak bölen (largest positive integer or polynomial) · cmn 最大公因數 /最大公因数 (largest positive integer or polynomial) · nl grootste gemene deler (largest positive integer or polynomial) · el μέγιστος κοινός διαιρέτης (largest positive integer or polynomial) · bg най-голям общ делител (largest positive integer or polynomial) · ko 최대공약수 (largest positive integer or polynomial) · ast máximu común divisor (largest positive integer or polynomial) · fr plus grand commun diviseur (largest positive integer or polynomial) · id faktor persekutuan terbesar (largest positive integer or polynomial) · ja 最大公約多項式 (largest positive integer or polynomial) · sv största gemensamma delare (largest positive integer or polynomial) · et suurim ühiskordne (largest positive integer or polynomial) · ka უდიდესი საერთო გამყოფი (largest positive integer or polynomial) · cmn 最大公約數 /最大公约数 (largest positive integer or polynomial) · gl máximo divisor común (largest positive integer or polynomial) · vi ước số chung lớn nhất (largest positive integer or polynomial) · pl największy wspólny dzielnik (largest positive integer or polynomial) · uk найбі́льший спі́льний дільни́к (largest positive integer or polynomial) · vi ước chung lớn nhất (largest positive integer or polynomial) · is stærsti samdeilir (largest positive integer or polynomial) · it massimo comun divisore (largest positive integer or polynomial) · es máximo común divisor (largest positive integer or polynomial) · it massimo comune divisore (largest positive integer or polynomial) · cs největší společný dělitel (largest positive integer or polynomial) · da største fælles divisor (largest positive integer or polynomial) · ml ഉത്തമ സാധാരണ ഘടകം (largest positive integer or polynomial) · cmn 最大公因子 (largest positive integer or polynomial) · de größter gemeinsamer Teiler (largest positive integer or polynomial) · tr ortak bölenlerin en büyüğü (largest positive integer or polynomial) · ca màxim comú divisor (largest positive integer or polynomial) · no største felles faktor (largest positive integer or polynomial) · hu legnagyobb közös osztó (largest positive integer or polynomial) · ru наибо́льший о́бщий дели́тель (largest positive integer or polynomial) · gl máximo común divisor (largest positive integer or polynomial) · ms faktor sepunya terbesar (largest positive integer or polynomial)