# greatest common divisor

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## great·est common divisor

(grā′tĭst)
n. Abbr. gcd
The largest number that divides evenly into each of a given set of numbers. Also called greatest common factor, highest common factor.

## greatest common divisor

n
(Mathematics) another name for highest common factor

## great′est com′mon divi′sor

n.
the largest number that is a common divisor of a given set of numbers. Abbr.: G.C.D. Also called great′est com′mon fac′tor.
ThesaurusAntonymsRelated WordsSynonymsLegend:
 Noun 1 greatest common divisor - the largest integer that divides without remainder into a set of integerscommon divisor, common factor, common measure - an integer that divides two (or more) other integers evenly
Translations
největší společný dělitel
suurin yhteinen tekijä

grootste gemene deler
största gemensamma delare
References in periodicals archive ?
In mathematics, the greatest common divisor (gcd) of two or more integers is the largest positive integer that divides the numbers without a remainder.
From the relationships (11) and (12) it follows that the polynomial cm(z) is the greatest common divisor of all elements of matrix C(z).
i] have greatest common divisor 1, we have [zeta] = 1 as a pole of order N + 1, and the other poles have order strictly less.
In Section 3, we discuss the concept of the greatest common divisors in the semimodules and show that for any Euclidean semimodule A in which every cyclic subsemimodule is subtractive, then every nonempty finite subset of A has a greatest common divisor.
Theorem 1 If c = a + b and d = gcd(a, b) the orbit of the billiard ball (on the corresponding table) passes through a lattice point (x, y) on the boundary if and only if d|x and d|y (gcd(a, b) denotes the greatest common divisor of a and b)
where C(s) is a left greatest common divisor of matrixes, and [?
To prove Corollary 2, note that the greatest common divisor of 4 and 6 is (4, 6) = 2, so from Corollary 1 we have the identity
He describes rings and fields, including linear equations in a field and vector spaces, polynomials over a field, factorization into primes, ideals and the greatest common divisor, solution of the general equation of nth degree, residual classes, extension fields, and isomorphisms.
Let denote [DELTA] the greatest common divisor of E and F, with E = [DELTA]E and F = [DELTA][?

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