What is the greatest common factor for 14 and 56?

Answer 1

since 14 = 14 x 1 and 56 = 14 x 4 the answer is 14, since it divides evenly into both and clearly nothing larger will.

There is a clever algorithm that can help you work this out in the general case:
GCD(14, 56) = GCD(14, 56 - 14) = GCD(14, 42)
This step (subtract the smaller from the larger) relies on the fact that any number that divides both 14 and 56 also divides 56 - 14.
Repeat this:
GCD(14, 42) = GCD(14, 42 - 14) = GCD(14, 28)
GCD(14, 28) = GCD(14, 28 - 14) = GCD(14, 14)
which is clearly 14.

This is called Euclid's Algorithm.