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.
Wiki User
∙ 2009-09-22 06:23:49The greatest common factor of 14 and 56 is 14.
The greatest common factor of 14 , 56 = 14
The greatest common factor of 56 & 70 is 14
The greatest common factor of 56 and 154 is 14
The Greatest common factor is 14.
The greatest common factor is 14.
The greatest common factor of 42 and 56 is 14.
The greatest common factor of 14, 28, and 70 is 14.
It is: 14
14.
The greatest common factor of 14, 56, and 63 is 7
14