The easiest way to find the factors of a pair of numbers, is simply to write out the factors until you find the ones that they have in common. So in this case, these factors would be listed as follows:
20: 1,2,4,5,10,20
50: 1,2,5,10,25,50.
From looking at these numbers, we can therefore see that the common factors are: 1,2,5,10