This page uses Euclid's algorithm.
This is an algorithm that can be used to find the highest common factor between two (or more) numbers. It relies on the principle that
if two numbers a and b share a common factor, then a-b (or b-a whichever is positive) also shares tha factor. This is because if a = p*k,
b = q*k, then:
a-b = p*k - q*k = k*(p-q).