Let R be a commutative ring. Let a and b be elements of R. We say that an element d of R is a greatest common divisor of a and b if 1. d divides a and d divides b, and 2. whenever an element r divides both a and b, then r also divides d. Show that if we have an equality of ideals (a,b)=(d) then d is a greatest common divisor of a and b. It follows that in a principal ideal domain, any two elements have at least one greatest common divisor.