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  2. Greatest common divisor - Wikipedia

    en.wikipedia.org/wiki/Greatest_common_divisor

    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.

  3. Euclidean algorithm - Wikipedia

    en.wikipedia.org/wiki/Euclidean_algorithm

    Synonyms for GCD include greatest common factor (GCF), highest common factor (HCF), highest common divisor (HCD), and greatest common measure (GCM). The greatest common divisor is often written as gcd( a , b ) or, more simply, as ( a , b ) , [ 3 ] although the latter notation is ambiguous, also used for concepts such as an ideal in the ring of ...

  4. Binary GCD algorithm - Wikipedia

    en.wikipedia.org/wiki/Binary_GCD_algorithm

    Visualisation of using the binary GCD algorithm to find the greatest common divisor (GCD) of 36 and 24. Thus, the GCD is 2 2 × 3 = 12.. 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.

  5. GCD matrix - Wikipedia

    en.wikipedia.org/wiki/GCD_matrix

    In mathematics, a greatest common divisor matrix (sometimes abbreviated as GCD matrix) is a matrix that may also be referred to as Smith's matrix. The study was initiated by H.J.S. Smith (1875). A new inspiration was begun from the paper of Bourque & Ligh (1992). This led to intensive investigations on singularity and divisibility of GCD type ...

  6. Solid Converter PDF - Wikipedia

    en.wikipedia.org/wiki/Solid_Converter_PDF

    Solid Converter PDF is document reconstruction software from Solid Documents which converts PDF files to editable formats. Originally released for the Microsoft Windows operating system, a Mac OS X version was released in 2010. The current versions are Solid Converter PDF 9.0 for Windows and Solid PDF to Word for Mac 2.1.

  7. Extended Euclidean algorithm - Wikipedia

    en.wikipedia.org/wiki/Extended_Euclidean_algorithm

    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 + = (,).

  8. GCD test - Wikipedia

    en.wikipedia.org/wiki/GCD_test

    A simple and sufficient test for the absence of a dependence is the greatest common divisor (GCD) test. It is based on the observation that if a loop carried dependency exists between X[a*i + b] and X[c*i + d] (where X is the array; a, b, c and d are integers, and i is the loop variable), then GCD (c, a) must divide (d – b).

  9. Order (group theory) - Wikipedia

    en.wikipedia.org/wiki/Order_(group_theory)

    Suppose G is a finite group of order n, and d is a divisor of n.The number of order d elements in G is a multiple of φ(d) (possibly zero), where φ is Euler's totient function, giving the number of positive integers no larger than d and coprime to it.

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