# Euclidean algorithm

Euclidean algorithm
noun Date: circa 1955 a method of finding the greatest common divisor of two numbers by dividing the larger by the smaller, the smaller by the remainder, the first remainder by the second remainder, and so on until exact division is obtained whence the greatest common divisor is the exact divisor — called also Euclid's algorithm

New Collegiate Dictionary. 2001.

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• Euclidean algorithm — In number theory, the Euclidean algorithm (also called Euclid s algorithm) is an algorithm to determine the greatest common divisor (GCD) of two elements of any Euclidean domain (for example, the integers). Its major significance is that it does… …   Wikipedia

• Euclidean algorithm — Algebra. a method based on the division algorithm for finding the greatest common divisor of two given integers. [1950 55] * * * ▪ mathematics       procedure for finding the greatest common divisor (GCD) of two numbers, described by the Greek… …   Universalium

• Euclidean algorithm — noun A method based on the division algorithm for finding the greatest common divisor (gcd) of two given integers …   Wiktionary

• Euclidean algorithm — Algebra. a method based on the division algorithm for finding the greatest common divisor of two given integers. [1950 55] …   Useful english dictionary

• Extended Euclidean algorithm — The extended Euclidean algorithm is an extension to the Euclidean algorithm for finding the greatest common divisor (GCD) of integers a and b : it also finds the integers x and y in Bézout s identity: ax + by = gcd(a, b). ,(Typically either x or… …   Wikipedia

• algorithm — [al′gə rith΄əm] n. [altered (after ARITHMETIC) < ALGORISM] 1. Math. a) any systematic method of solving a certain kind of problem b) the repetitive calculations used in finding the greatest common divisor of two numbers: called in full… …   English World dictionary

• Euclidean domain — In abstract algebra, a Euclidean domain (also called a Euclidean ring) is a type of ring in which the Euclidean algorithm applies. A Euclidean domain is a specific type of integral domain, and can be characterized by the following (not… …   Wikipedia

• Euclidean — List of topics named after Euclid (Euclidean or, less commonly, Euclidian) *Euclidean space *Euclidean geometry *Euclid s Elements *Euclidean domain *Euclidean distance *Euclidean ball *Euclidean algorithm *Euclidean distance map *Extended… …   Wikipedia

• Algorithm — Flow chart of an algorithm (Euclid s algorithm) for calculating the greatest common divisor (g.c.d.) of two numbers a and b in locations named A and B. The algorithm proceeds by successive subtractions in two loops: IF the test B ≤ A yields yes… …   Wikipedia

• Algorithm characterizations — The word algorithm does not have a generally accepted definition. Researchers are actively working in formalizing this term. This article will present some of the characterizations of the notion of algorithm in more detail. This article is a… …   Wikipedia