GCD Computation of n Integers

TL;DR

This paper introduces extended algorithms for computing the GCD of multiple integers, building upon Euclid's and binary GCD algorithms, to improve efficiency in algorithmic number theory applications.

Contribution

It presents novel extensions of Euclid's and binary GCD algorithms for calculating the GCD of more than two integers.

Findings

Extended Euclid's algorithm for n integers

Extended binary GCD algorithm for n integers

Potential efficiency improvements in multi-integer GCD computations

Abstract

Greatest Common Divisor (GCD) computation is one of the most important operation of algorithmic number theory. In this paper we present the algorithms for GCD computation of $n$ integers. We extend the Euclid's algorithm and binary GCD algorithm to compute the GCD of more than two integers.