In mathematics, the greatest common divisor (GCD), also known as greatest common factor (GCF), of two or more integers, which are not all zero, is the...

In algebra, the greatest common divisor (frequently abbreviated as GCD) of two polynomials is a polynomial, of the highest possible degree, that is a...

several ways to compute least common multiples. The least common multiple can be computed from the greatest common divisor (gcd) with the formula lcm ⁡...

properties such as the existence of a Euclidean algorithm for computing greatest common divisors, Bézout's identity, the principal ideal property, Euclid's lemma...

or Euclid's algorithm, is an efficient method for computing the greatest common divisor (GCD) of two integers, the largest number that divides them both...

following theorem: Bézout's identity—Let a and b be integers with greatest common divisor d. Then there exist integers x and y such that ax + by = d. Moreover...

extension to the Euclidean algorithm, and computes, in addition to the greatest common divisor (gcd) of integers a and b, also the coefficients of Bézout's identity...

In mathematics, a divisor of an integer n , {\displaystyle n,} also called a factor of n , {\displaystyle n,} is an integer m {\displaystyle m} that may...

lowest common multiple of the denominators of a set of fractions Greatest common divisor, the largest positive integer that divides each of the integers...

quotients of a and b (respectively) by the greatest common divisor of a and b. Proof: If d is this greatest common divisor, Bézout's identity asserts the existence...

expressing this fact in mathematical notation is to indicate that their greatest common divisor is one, by the formula gcd(a, b) = 1 or (a, b) = 1. In their 1989...

phrase least common divisor is a confusion of the following two distinct concepts in arithmetic: Least common multiple Greatest common divisor This disambiguation...

implemented recursively. The Euclidean algorithm, which computes the greatest common divisor of two integers, can be written recursively. Function definition:...

binary Euclidean algorithm, is an algorithm that computes the greatest common divisor (GCD) of two nonnegative integers. Stein's algorithm uses simpler...

factorization domains (UFD). Greatest common divisors exist in UFDs, but not every integral domain in which greatest common divisors exist (known as a GCD domain)...

Pythagorean theorem, Thales' theorem, the Euclidean algorithm for greatest common divisors, Euclid's theorem that there are infinitely many prime numbers...

CA]. Tomas Garcia, Rogelio (August 2020). "Equalities between greatest common divisors involving three coprime pairs" (PDF). Notes on Number Theory and...

preorder defined by the degree. Given a greatest common divisor of two polynomials, the other greatest common divisors are obtained by multiplication by a...

In compiler theory, a greatest common divisor test (GCD test) is the test used in study of loop optimization and loop dependence analysis to test the...

if and only if a and b are coprime, that is, if a and b have a greatest common divisor of 1. In higher mathematics, "irreducible fraction" may also refer...

other tasks. The following Gödel module is a specification of the greatest common divisor (GCD) of two numbers. It is intended to demonstrate the declarative...

dc (desk calculator) is a cross-platform reverse-Polish calculator which supports arbitrary-precision arithmetic. It was written by Lorinda Cherry and...

the number of integers k in the range 1 ≤ k ≤ n for which the greatest common divisor gcd(n, k) is equal to 1. The integers k of this form are sometimes...

generally, with coefficients in a unique factorization domain) is the greatest common divisor of its coefficients. The primitive part of such a polynomial is...

by c to give the reduced fraction ⁠d/e⁠. If one takes for c the greatest common divisor of the numerator and the denominator, one gets the equivalent fraction...

particularly ring theory, maximal common divisors are an abstraction of the number theory concept of greatest common divisor (GCD). This definition is slightly...

The integers are usually written in lowest terms, i.e. their greatest common divisor should be 1. Miller indices are also used to designate reflections...

generalization of both Euclid's algorithm for computing polynomial greatest common divisors, and Gaussian elimination for linear systems. Gröbner bases were...

. Compute K = gcd ( a , N ) {\displaystyle K=\gcd(a,N)} , the greatest common divisor of a {\displaystyle a} and N {\displaystyle N} . If K ≠ 1 {\displaystyle...

if their greatest common divisor, and simultaneously their only divisor, is 1. The Euclidean algorithm computes the greatest common divisor of two integers...