1. The problem statement, all variables and given/known data If A is a set of integers and B is a set properly contained in A, does the greatest common denominator of all of the integers in A divide the greatest common denominator of all elements in B? 2. Relevant equations None. 3. The attempt at a solution Obviously gcd(A) divides any element of B, since anything in B is contained is also in A, but I can't get from there to anything about the relationship between gcd(A) and gcd(B).