Finding the Greatest Common Divisor by Repeated Subtractions

The greatest common divisor (GCD) of two or more positive integers is the largest integer that is a common divisor of the given integers - i.e. the largest integer that divides the given integers without leaving a remainder. There are many methods for finding the GCD of two or more integers. Some of the most commonly taught in schools are the methods of factor listing, prime factorisation, and common decomposition using the so-called ladder method. Each of these methods is briefly illustrated below for the pair of integers 18 and 24.