Algorithm and bound for the greatest common divisor of n integers

Abstract

A new version of the Euclidean algorithm for finding the greatest common divisor of n integers a _i and multipliers x _i such that gcd = x ₁ a ₁ + ··· + x _n a _n is presented. The number of arithmetic operations and the number of storage locations are linear in n . A theorem of Lamé that gives a bound for the number of iterations of the Euclidean algorithm for two integers is extended to the case of n integers. An algorithm to construct a minimal set of multipliers is presented. A Fortran program for the algorithm appears as Comm. ACM Algorithm 386.