1. The problem statement, all variables and given/known data if 1 = gcd(a,b), show that gcd(ac,b) = gcd(c,b) 2. Relevant equations None 3. The attempt at a solution My attempt at a solution: Let d = gcd(ac,b), Let g = gcd(c,b), I want to show that g|d and that d|g. I then went on to make a bunch of circular writing and get nowhere... I set up things like: 1 = ax + by d = acw + bz --> 1 = (ac/d)w + (b/d)z g = cn + bm --> 1 = (c/d)n + (b/d)m Is my approach here a solid method? I can't think of any other way to show that gcd(ac,b) = gcd(c,b) besides assigning each of them a value and showing that they divide eachother.