Is 440 a factor of 72840?

Question

I would like to know how to solve the following question: Is 440 a factor of 72840? I would have thought that this involves dividing 72840 by 440 and seeing if it produces an integer. However, the solution I have in front of me says "If 440 is a factor of 72840, then all prime factors of 440 should also be prime factors of 72840". So it asking us to find the prime factors of both numbers. Now, this seems strange because it is a GRE question and therefore should be quite simple. However, 607 is a factor of 72840. I can't imagine having to check if 607 is a prime (which it is) on a GRE test. Shouldn't it suffice to divide 72840 by 440 to see if it produces an integer? Or am I wrong in thinking that?

Answer 1

Both answers are correct, but the simpler of the two is dividing 72840÷440. If there is no remainder, it is a factor. The same holds true for 607, even though it is prime.