If x and y are positive integers, which of the following CANNOT be the greatest common divisor of 35x and 20y?

I am just going to do whatever I can to either prove that each can be or cannot be the greatest common divisor. Whatever I can could be algebra, substituting numbers or anything else that gets this done.


A) 5 If x = 1 and y = 1, then this is the greatest common divisor. (Keepin' it simple.)

B) 5(x - y) If x = 3 and y = 2, this is the greatest common divisor. (I messed around with x = 2 and y = 1 first. When that didn't work, I bumped up to 3 and 2.)

C) 20x If I divide 35x by 20x, I get 35/20 = 7/4. So 20x cannot be a divisor of 35x. I could also just try using any positive integer for x and soon realize that whatever I use I can't evenly divide 35x by 20x. (So this is the answer, and the question is done. For illustrative purposes, and to check my answer, I'll check the other two as well.)

D) 20y If y = 7 and x = 4, then 20y = 35x = 140, and 20y is the greatest common divisor.

E) 35x If x = 4 and y = 7, then 35x = 20y = 140, and 35x is the greatest common divisor. (Hah, a repeat. Always nice.)

So C it is.