The answer is 5. In order to get here, you must list all possible factors of each number.
For 150, the factors are:
1,2,3,5,6,10,15,25,30,50,75,150
For 275, the factors are:
1,5,11,25,55,275
For 420, the factors are:
1,2,3,4,5,6,7,10,12,14,15,20,21,28,30,35,42,60,70,84,105,140,210,420
As you can see, the greatest factor all three of these numbers have is 5.