When you see a fraction, you see a numerator and a denominator. To find the common factor, see whichever number among these is least: The numerator, the denominator or the difference between numerator and denominator.
Fortunately for me, a wonderful 3rd grade teacher gave us the solution. It helped that he was male, and my 8-year-old daughter had a major crush on him. She ate up every word that man said, so when he taught her to skip count to some familiar tunes she came home singing her math just for fun.