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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 ...
In number theory, the gcd-sum function, [1] also called Pillai's arithmetical function, [1] is defined for every by = = (,) or ... Code of Conduct; Developers;
The greatest common divisor (GCD) of integers a and b, at least one of which is nonzero, is the greatest positive integer d such that d is a divisor of both a and b; that is, there are integers e and f such that a = de and b = df, and d is the largest such integer.
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
Euclid's method for finding the greatest common divisor (GCD) of two starting lengths BA and DC, both defined to be multiples of a common "unit" length. The length DC being shorter, it is used to "measure" BA, but only once because the remainder EA is less than DC. EA now measures (twice) the shorter length DC, with remainder FC shorter than EA.
GCD was first released with Mac OS X 10.6, and is also available with iOS 4 and above. The name "Grand Central Dispatch" is a reference to Grand Central Terminal. [citation needed] The source code for the library that provides the implementation of GCD's services, libdispatch, was released by Apple under the Apache License on September 10, 2009 ...
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 .
The following Gödel module is a specification of the greatest common divisor (GCD) of two numbers. It is intended to demonstrate the declarative nature of Gödel, not to be particularly efficient. The CommonDivisor predicate says that if i and j are not zero, then d is a common divisor of i and j if it lies between 1 and the smaller of i and j ...