To start, look at the factors of the smallest number: in this case, 50. The factors of 50 are: 1,2,5,10,25,50. Moving to the next smallest number, 125, the factors are: 1,5,25,125. The final number, 275, has factors of: 1,5,11,25,55,275. Looking at all three of these numbers, the common factors are: 1,5,25. The greatest common factor, then, is 25.