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 ⁡...

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...

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

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

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...

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

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...

polynomial with integer coefficients is primitive if it has 1 as a greatest common divisor of its coefficients.) A corollary of Gauss's lemma, sometimes also...

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

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...

concerning integers, such as the Euclidean algorithm for finding the greatest common divisor of two integers, and modular arithmetic, for which only remainders...

the largest possible number of people. Anomalous cancellation Greatest common divisor Partial fraction decomposition, reverses the process of adding...

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

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

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

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

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

provide a geometrical method to determine the least common multiple and the greatest common divisor of two natural numbers by making use of reflections...

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)...

greatest common divisor (although it may not be possible to find it using the Euclidean algorithm). If x and y are elements of a PID without common divisors...

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

numbers, while its greatest element is 0, which is divisible by all natural numbers. The meet operation is greatest common divisor while the join operation...

. 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...

those of f, and the greatest common divisor of two polynomials is independent of the ambient field, so the greatest common divisor of f and f′ has coefficients...