Linda Eroh

Date of Defense

8-3-1993

Department

Mathematics

First Advisor

John Petro, Mathematics and Statistics

Second Advisor

Thomas Richardson, Mathematics and Statistics

Third Advisor

Naveed Sherwani, Computer Science

Keywords

Euclid's algorithm, greatest common factor, highest common factor, GCF, HCF

Abstract

The Euclidian algorithm, one of the oldest known algorithms in mathematics, finds the greatest common divisor (gcd) of a pair of integers. First described in Euclid's Elements, this algorithm has since been adapted to find the gcd of two polynomials with coefficients taken from a field and to find a linear combination of two integers or of two polynomials which yields their gcd. In this paper we address several questions concerning the problem of finding the gcd of a list of more than two integers. First, is there a best or most efficient way to find the gcd of a list of integers? For instance, can we find the gcd more efficiently by considering the integers two at a time or by considering the entire list at once? Is the efficiency of our algorithm improved if we start with the smallest integer in the list? What value do we most often expect for the gcd of a list of integers; specifically, what is the probability that it be the universal divisor 1? In this paper, we analyze three algorithms to find the gcd of a list of integers. Each algorithm is a simple modification of the classical Euclidean algorithm. For each algorithm, we find a bound for the theoretical worst case and compute experimental estimates of the algorithm's complexity using Maple.

Access Setting

Honors Thesis-Campus Only

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