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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. 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 ...

  4. 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 ...

  5. 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.

  6. Table of prime factors - Wikipedia

    en.wikipedia.org/wiki/Table_of_prime_factors

    m and n are coprime (also called relatively prime) if gcd(m, n) = 1 (meaning they have no common prime factor). lcm(m, n) (least common multiple of m and n) is the product of all prime factors of m or n (with the largest multiplicity for m or n). gcd(m, n) × lcm(m, n) = m × n. Finding the prime factors is often harder than computing gcd and ...

  7. Bézout domain - Wikipedia

    en.wikipedia.org/wiki/Bézout_domain

    Also, since R is a Bézout domain, the gcd d in R of the constant terms a 0 and b 0 lies in a 0 R + b 0 R. Since any element without constant term, like a − a 0 or b − b 0 , is divisible by any nonzero constant, the constant d is a common divisor in S of a and b ; we shall show it is in fact a greatest common divisor by showing that it lies ...

  8. Lehmer's GCD algorithm - Wikipedia

    en.wikipedia.org/wiki/Lehmer's_GCD_algorithm

    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 .

  9. Gaussian integer - Wikipedia

    en.wikipedia.org/wiki/Gaussian_integer

    As for any unique factorization domain, a greatest common divisor (gcd) of two Gaussian integers a, b is a Gaussian integer d that is a common divisor of a and b, which has all common divisors of a and b as divisor. That is (where | denotes the divisibility relation), d | a and d | b, and; c | a and c | b implies c | d.