# 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
Collins English Dictionary – Complete and Unabridged, 12th Edition 2014 © HarperCollins Publishers 1991, 1994, 1998, 2000, 2003, 2006, 2007, 2009, 2011, 2014

## 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
Based on WordNet 3.0, Farlex clipart collection. © 2003-2012 Princeton University, Farlex Inc.
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).
So if g is the greatest common divisor of the [[alpha].sub.i] (which can be computed in polynomial time), and [alpha]/g = [[[alpha].sub.1]/g, [[alpha].sub.2]/g, ..., [[alpha].sub.N+1]/g] the formula E([alpha])(gt) = E([alpha]/g)(t) holds, and we may assume that the numbers [[alpha].sub.i] span Z without changing the complexity of the problem.
We use the definition as in ; for any arbitrary n x n matrix A, form the characteristic matrix x[I.sub.n] - A and let [d.sub.j](x) denote the greatest common divisor (gcd) of all minors of order j of x[I.sub.n] - A, j = 1,2, ..., n.
We say that Y is an indecomposable curve of canonical type if [K.sub.X] x [Y.sub.i] = Y x [Y.sub.i] = 0 for every i, SuppY is connected, and the greatest common divisor of integers [n.sub.1,] ..., [n.sub.k] is equal to one.
Figure 4: The first seven members of the aliquot sequence of 30: sum of proper integer proper divisors divisors 30 1, 2, 3, 5, 6, 10, 15 42 42 1, 2, 3, 6, 7, 14, 21 54 54 1, 2, 3, 6, 9, 18, 27 66 66 1, 2, 3, 6, 11, 22, 33 78 78 1, 2, 3, 6, 13, 26, 39 90 90 1, 2, 3, 5, 6, 9, 10, 15, 18, 30, 144 45 144 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 259 24, 36, 48, 72 What is striking about the sequence {30, 42, 54, 66, 78, 90, 144} is that the Greatest Common Divisor (CGD) for its 7 members is 6, which is a 'perfect number' because it equals the sum of its proper divisors (1+2+3=6).
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)
They studied the necessary and sufficient condition under which from p-periodicity and q-periodicity we can derive gcd(p, q)-periodicity (recall that gcd is the greatest common divisor).
where C(s) is a left greatest common divisor of matrixes, and [??](s) and [??](s) are mutually distinct.

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