Meanings
plural greatest common divisors
- arithmeticThe 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).
The greatest common divisor of 66, 30 and 18 is 6.
3 more examples
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 53This 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 187Synonyms: gcd, greatest common factor, highest common factor, greatest common denominator
Synonyms & antonyms
nounThe 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).
antonym(s) of “largest number that divides each of a set of positive integers”
More synonyms by meaning
nounthe largest integer that divides without remainder into a set of integers
Synonym sets from Open English WordNet, CC BY 4.0.
Translations
Bulgarian най-голям общ делител
- най-голям общ делител (naj-goljam obšt delitel)largest positive integer or polynomial
Catalan màxim comú divisor
- màxim comú divisorlargest positive integer or polynomial
Chinese Mandarin 最大公因子, 最大公約數 /最大公约数
- 最大公因子 (zuìdà gōngyīnzǐ)largest positive integer or polynomial
- 最大公約數 /最大公约数 (zuìdà gōngyuēshù)largest positive integer or polynomial
- 最大公因數 /最大公因数 (zuìdà gōngyīnshù)largest positive integer or polynomial
Czech největší společný dělitel
- největší společný dělitellargest positive integer or polynomial
Danish største fælles divisor
- største fælles divisorlargest positive integer or polynomial
Dutch grootste gemene deler
- grootste gemene delerlargest positive integer or polynomial
Estonian suurim ühiskordne
- suurim ühiskordnelargest positive integer or polynomial
Finnish suurin yhteinen tekijä
- suurin yhteinen tekijälargest positive integer or polynomial
French plus grand commun diviseur
- plus grand commun diviseurlargest positive integer or polynomial
German größter gemeinsamer Teiler
- größter gemeinsamer Teilerlargest positive integer or polynomial
Greek μέγιστος κοινός διαιρέτης
- μέγιστος κοινός διαιρέτης (mégistos koinós diairétis)largest positive integer or polynomial
Hungarian legnagyobb közös osztó
- legnagyobb közös osztólargest positive integer or polynomial
Icelandic stærsti samdeilir, stærsti sameiginlegi deilir
- stærsti samdeilirlargest positive integer or polynomial
- stærsti sameiginlegi deilirlargest positive integer or polynomial
Indonesian faktor persekutuan terbesar
- faktor persekutuan terbesarlargest positive integer or polynomial
Italian massimo comun divisore, massimo comune divisore
- massimo comun divisorelargest positive integer or polynomial
- massimo comune divisorelargest positive integer or polynomial
Japanese 最大公約数, 最大公約多項式
- 最大公約数 (saidai kōyakusū)largest positive integer or polynomial
- 最大公約多項式 (saidai kōyaku takōshiki)largest positive integer or polynomial
Korean 최대공약수
- 최대공약수 (choedaegong'yaksu)largest positive integer or polynomial
Malay faktor sepunya terbesar
- faktor sepunya terbesarlargest positive integer or polynomial
Norwegian største felles faktor, største felles nevner
- største felles faktorlargest positive integer or polynomial
- største felles nevnerlargest positive integer or polynomial
Polish największy wspólny dzielnik
- największy wspólny dzielniklargest positive integer or polynomial
Portuguese máximo divisor comum
- máximo divisor comumlargest positive integer or polynomial
Romanian cel mai mare divizor comun, c.m.m.d.c
- cel mai mare divizor comunlargest positive integer or polynomial
- c.m.m.d.clargest positive integer or polynomial
Russian наибо́льший о́бщий дели́тель
- наибо́льший о́бщий дели́тель (naibólʹšij óbščij delítelʹ)largest positive integer or polynomial
Spanish máximo común divisor
- máximo común divisorlargest positive integer or polynomial
Swedish största gemensamma delare
- största gemensamma delarelargest positive integer or polynomial
Thai ตัวหารร่วมมาก
- ตัวหารร่วมมาก (dtuua-hǎan-rûuam-mâak)largest positive integer or polynomial
Turkish en büyük ortak bölen, ortak bölenlerin en büyüğü
- en büyük ortak bölenlargest positive integer or polynomial
- ortak bölenlerin en büyüğülargest positive integer or polynomial
Ukrainian найбі́льший спі́льний дільни́к
- найбі́льший спі́льний дільни́к (najbílʹšyj spílʹnyj dilʹnýk)largest positive integer or polynomial
Vietnamese ước chung lớn nhất, ước số chung lớn nhất
- ước chung lớn nhấtlargest positive integer or polynomial
- ước số chung lớn nhấtlargest positive integer or polynomial
Cite this entry
greatest common divisor. (n.d.). In WatkinsX Dictionary. Retrieved November 5, 2026, from https://dictionary.watkinsx.com/word/greatest%20common%20divisor
“greatest common divisor.” WatkinsX Dictionary, https://dictionary.watkinsx.com/word/greatest%20common%20divisor. Accessed November 5, 2026.
WatkinsX Dictionary, s.v. “greatest common divisor,” accessed November 5, 2026, https://dictionary.watkinsx.com/word/greatest%20common%20divisor.
Source: greatest common divisor on Wiktionary, CC BY-SA 4.0.