Search results
Results From The WOW.Com Content Network
The Euclidean domains and the UFD's are subclasses of the GCD domains, domains in which a greatest common divisor of two numbers always exists. [153] In other words, a greatest common divisor may exist (for all pairs of elements in a domain), although it may not be possible to find it using a Euclidean algorithm.
Animation showing an application of the Euclidean algorithm to find the greatest common divisor of 62 and 36, which is 2. A more efficient method is the Euclidean algorithm , a variant in which the difference of the two numbers a and b is replaced by the remainder of the Euclidean division (also called division with remainder ) of a by b .
In arithmetic and computer programming, the extended Euclidean algorithm is an 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, which are integers x and y such that
Lehmer's GCD algorithm, named after Derrick Henry Lehmer, is a fast GCD algorithm, an improvement on the simpler but slower Euclidean algorithm. It is mainly used for big integers that have a representation as a string of digits relative to some chosen numeral system base , say β = 1000 or β = 2 32 .
Lamé's Theorem is the result of Gabriel Lamé's analysis of the complexity of the Euclidean algorithm.Using Fibonacci numbers, he proved in 1844 [1] [2] that when looking for the greatest common divisor (GCD) of two integers a and b, the algorithm finishes in at most 5k steps, where k is the number of digits (decimal) of b.
This template shows a step by step illustration of the Euclidean algorithm. It is meant to illustrate the Euclidean algorithm article. This template depends on the Calculator gadget. If that gadget is not enabled, or js is not supported (e.g. when printing) the template is invisible.
English: An abstract syntax tree for the following pseudocode, implementing the Euclidean algorithm to find the greatest common divisor of a and b: while b ≠ 0 : if a > b : a := a - b else : b := b - a return a
The binary GCD algorithm, also known as Stein's algorithm or the binary Euclidean algorithm, [1] [2] is an algorithm that computes the greatest common divisor (GCD) of two nonnegative integers. Stein's algorithm uses simpler arithmetic operations than the conventional Euclidean algorithm ; it replaces division with arithmetic shifts ...