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Let Eulen(a,b) denote the length of the Euclidean algorithm for a pair a,b. Eulen(2322, 654) = 6, Eulen(30, 6) = 1. I'll use this notation in the proof of the following very important consequence of the algorithm:
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www.cut-the-knot.org/blue/Euclid.shtml
www.cut-the-knot.org/blue/Euclid.shtml
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Find the Greatest common Divisor...
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www.math.sc.edu/~sumner/numbertheory/euclidean/euclidea...
www.math.sc.edu/~sumner/numbertheory/euclidean/euclidean.html
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This computes the greatest common divisor of two given integers via the Euclidean Algorithm, showing all the steps. The greatest common divisor is explicitly noted at the bottom.
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www.math.umn.edu/~garrett/crypto/a01/Euclid.html
www.math.umn.edu/~garrett/crypto/a01/Euclid.html
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There are even principal rings which are not Euclidean but where the equivalent of the Euclidean algorithm can be defined. The algorithm for rational ...
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mathworld.wolfram.com/EuclideanAlgorithm.html
mathworld.wolfram.com/EuclideanAlgorithm.html
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You then repeatedly divide the previous divisor by the previous remainder until there is no remainder. The last remainder you divided by is the greatest common divisor. We illustrate the Euclidean algorithm in computing gcd(77,52).
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www.math.ksu.edu/~bennett/gc/831.html
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Definition: An algorithm to compute the greatest common divisor of two positive integers. It is Euclid(a,b){if (b=0) then return a; else return Euclid(b, a mod b);}. The run time complexity is O((log a)(log b)) bit operations. ... Also known as Euclidean algorithm.
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www.itl.nist.gov/div897/sqg/dads/HTML/euclidalgo.html
www.itl.nist.gov/div897/sqg/dads/HTML/euclidalgo.html
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The Euclidean Algorithm proceeds by dividing by , with remainder, then dividing the divisor by the remainder, and repeating this process until the remainder is zero. The greatest common factor of and is the last divisor.
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www.math.utah.edu/online/1010/euclid/
www.math.utah.edu/online/1010/euclid/
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Euclidean algorithm summary with 9 pages of encyclopedia entries, essays, summaries, research information, and more. ... Euclidean algorithm: Plot of the running time for gcd(x,y)
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www.bookrags.com/Euclidean_algorithm
www.bookrags.com/Euclidean_algorithm
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