Noun
(historical) Any of certain algorithms first described in Euclid's Elements.
(arithmetic, number theory) Specifically, a method, based on a division algorithm, for finding the greatest common divisor (gcd) of two given integers; any of certain variations or generalisations of said method.
Source: en.wiktionary.orgA key advantage of the Euclidean algorithm is that it can find the GCD efficiently without having to compute the prime factors. Source: Internet
After each step k of the Euclidean algorithm, the norm of the remainder f(r k ) is smaller than the norm of the preceding remainder, f(r k−1 ). Source: Internet
Description Procedure The Euclidean algorithm proceeds in a series of steps such that the output of each step is used as an input for the next one. Source: Internet
History An early example of algorithm complexity analysis is the running time analysis of the Euclidean algorithm done by Gabriel Lamé in 1844. Source: Internet
If both a and b are nonzero, the extended Euclidean algorithm produces one of the two pairs such that and (equality may occur only if one of a and b is a multiple of the other). Source: Internet
In particular, he gave an algorithm for computing the greatest common divisor of two numbers (the Euclidean algorithm ; Elements, Prop. VII.2) and the first known proof of the infinitude of primes (Elements, Prop. IX.20). Source: Internet