First, let's list the factors of each number
150: 1, 150, 2, 75, 3, 50, 5, 30, 6, 25, 10, 15
135: 1, 135, 3, 45, 5, 27, 9, 15
From these lists, we can say for certain that 1, 3, 5, and 15 go into both numbers, so that would be your list of the common factors.
I hope this helps!