Phrase guide

greatest common divisor

noun · 2 senses · updated from the 2026-07-25 local source snapshot

Definitions and examples are grouped by meaning. Pronunciation, history, word forms, translations, descendants, synonyms, antonyms, derived terms, and related words appear whenever the source provides them.

Sound

Pronunciation

Each Play button uses your device's default local English voice, or a natural local fallback. The selected voice name appears after playback. This is synthesized speech, not a source recording.

  • Received-Pronunciation: /ˈɡɹeɪ.tɪst ˈkɒm.ən dɪˈvaɪ.zə/
  • UK: Recorded audio is listed in the source snapshot.
  • General-American: /ˈɡɹeɪ.tɪst ˈkɑ.mɪn dɪˈvaɪ.zɚ/

1

noun

Meaning 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).

Definition source: English Wiktionary via Wiktextract

Topics: arithmetic, mathematics, number-theory, sciences

Examples

  • The greatest common divisor of 66, 30 and 18 is 6.
  • 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.

Meaning relationships

Synonyms: none provided

Antonyms: none provided

2

noun

Meaning 2

the largest integer that divides without remainder into a set of integers

Definition source: Princeton WordNet 3.0

No example sentence was provided for this meaning.

Meaning relationships

Synonyms: greatest common factor, highest common factor

Antonyms: none provided

Broader terms: common divisor, common factor, common measure

History

Etymology

No etymology was provided for this word.

Across languages

Translations

44 source translations are retained for this English entry.

  • Asturian: máximu común divisor — largest positive integer or polynomial
  • Azerbaijani: ən böyük ortaq bölən — largest positive integer or polynomial
  • Bulgarian: най-голям общ делител (naj-goljam obšt delitel) — largest positive integer or polynomial
  • Catalan: màxim comú divisor — largest positive integer or polynomial
  • Chinese Mandarin: 最大公因子 (zuìdà gōngyīnzǐ) — largest positive integer or polynomial
  • Chinese Mandarin: 最大公約數 /最大公约数 (zuìdà gōngyuēshù) — largest positive integer or polynomial
  • Chinese Mandarin: 最大公因數 /最大公因数 (zuìdà gōngyīnshù) — largest positive integer or polynomial
  • Czech: největší společný dělitel — largest positive integer or polynomial
  • Danish: største fælles divisor — largest positive integer or polynomial
  • Dutch: grootste gemene deler — largest positive integer or polynomial
  • Estonian: suurim ühiskordne — largest positive integer or polynomial
  • Finnish: suurin yhteinen tekijä — largest positive integer or polynomial
  • French: plus grand commun diviseur — largest positive integer or polynomial
  • Galician: máximo común divisor — largest positive integer or polynomial
  • Galician: máximo divisor común — largest positive integer or polynomial
  • Georgian: უდიდესი საერთო გამყოფი (udidesi saerto gamq̇opi) — largest positive integer or polynomial
  • German: größter gemeinsamer Teiler — largest positive integer or polynomial
  • Greek: μέγιστος κοινός διαιρέτης (mégistos koinós diairétis) — largest positive integer or polynomial
  • Hungarian: legnagyobb közös osztó — largest positive integer or polynomial
  • Icelandic: stærsti samdeilir — largest positive integer or polynomial
  • Icelandic: stærsti sameiginlegi deilir — largest positive integer or polynomial
  • Indonesian: faktor persekutuan terbesar — largest positive integer or polynomial
  • Italian: massimo comun divisore — largest positive integer or polynomial
  • Italian: massimo comune divisore — largest positive integer or polynomial
  • Japanese: 最大公約数 (saidai kōyakusū) — largest positive integer or polynomial
  • Japanese: 最大公約多項式 (saidai kōyaku takōshiki) — largest positive integer or polynomial
  • Korean: 최대공약수 (choedaegong'yaksu) — largest positive integer or polynomial
  • Malay: faktor sepunya terbesar — largest positive integer or polynomial
  • Malayalam: ഉത്തമ സാധാരണ ഘടകം (uttama sādhāraṇa ghaṭakaṁ) — largest positive integer or polynomial
  • Norwegian: største felles faktor — largest positive integer or polynomial
  • Norwegian: største felles nevner — largest positive integer or polynomial
  • Polish: największy wspólny dzielnik — largest positive integer or polynomial
  • Portuguese: máximo divisor comum — largest positive integer or polynomial
  • Romanian: cel mai mare divizor comun — largest positive integer or polynomial
  • Romanian: c.m.m.d.c — largest positive integer or polynomial
  • Russian: наибо́льший о́бщий дели́тель (naibólʹšij óbščij delítelʹ) — largest positive integer or polynomial
  • Spanish: máximo común divisor — largest positive integer or polynomial
  • Swedish: största gemensamma delare — largest positive integer or polynomial
  • Thai: ตัวหารร่วมมาก (dtuua-hǎan-rûuam-mâak) — largest positive integer or polynomial
  • Turkish: en büyük ortak bölen — largest positive integer or polynomial
  • Turkish: ortak bölenlerin en büyüğü — largest positive integer or polynomial
  • Ukrainian: найбі́льший спі́льний дільни́к (najbílʹšyj spílʹnyj dilʹnýk) — largest positive integer or polynomial
  • Vietnamese: ước chung lớn nhất — largest positive integer or polynomial
  • Vietnamese: ước số chung lớn nhất — largest positive integer or polynomial