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A Study of Euclidean K-Ary Gcd Algorithm

Nikolai Andreevich Antonov, Shamil Talgatovich Ishmukhametov, Al Halidi Arkan M, Mariia Evgenevna Maiorova


The problem of computing the greatest common divisor GCD of natural numbers is one of the most common problems that is solved in modern computational mathematics and its applications. At the moment, many algorithms are known to solve this problem, but every day the requirements for the effectiveness of such algorithms become more stringent. As a result, there is a need to create new algorithms that are more efficient in time and number of the operations performed. Besides, they must allow the possibility of their transformation into modern programming languages while maintaining the efficiency of the algorithm.

This article presents an analysis of the realization features and the results of testing the speed of three GCD computation algorithms: the classical Euclidean algorithm, the Sorenson k-ary algorithm, and the approximating k-ary algorithm developed by the second of the authors in MicrosoftVisualStudio in C #. Qualitative and quantitative data on the effectiveness of these algorithms in terms of time and number of the steps within the main cycle are have been obtained.

The concluding part of the article contains the analysis of the results obtained, their representation in the diagrams, and gives the recommendations on the choice of the parameters of the methods.


s: GCD of natural numbers, Euclidian GCD algorithm, k-ary GCD algorithm, approximating k-ary algorithm

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