Find the square root of the first number, rounding down. You can do this on a calculator with a square root key. For example, suppose you want to find the GCF of 54 and 68. The square root of 54 is 7.35, so round this down to 7.
Divide the first number by 2. If there is no remainder, write down 2 and the quotient (the answer you calculated). In the example. 54/2 = 27 with no remainder, so write 2 and 27.
Repeat this with all the whole numbers from 2 to the result in Step 1. If there is no remainder, add the divisor and the quotient -- that is, the number you divided by and the answer you got -- to the list. In the example, 54/3 = 18 with no remainder, so add 3 and 18 to the list, which is now 2, 27, 3, 18.
Dividing 54 by 4 leaves a remainder, but 54/6 = 9 with no remainder, so add those to the list, which is now 2, 27, 3, 18, 6, 9. Dividing 54 by 7 leaves a remainder, so you are done.
Repeat Steps 1, 2 and 3 with the second number. In the example, the square root of 68 is 8.2, which you would round down to 8. Then 68/2 = 34 with no remainder; 68/3 has a remainder; 68/4 = 17 with no remainder; and 68/5, 68/6 68/7 and 68/8 each leave remainders, so the second list is 2, 34, 4, 17.
Find the largest number that is on both lists. This is the GCF or greatest common factor. In the example, the largest number on both lists is 2.