How do you find the greatest common divisor of 85 and 102?

Answer 1

Divide the larger number by the smaller one and then replace the larger by the remainder. Repeat until a remainder is 0 or both numbers are 1. In the first case, the non-zero number is the GCD, in the other case, the numbers are coprme: GCD = 1.

Thus GCD(85, 102)

102 = 1*85 + R = 17

so GCD(85, 17)

85 = 5*17 + R = 0

so GCD(0, 17) therefore 17.

= GCD[85, (102-85)] = GCD(85, 17)

Answer 2

The GCF is 17.