What is Euclid's Algorithm?

Answer 1

Euclid's algorithm is a popular algorithm to compute the GCD of two numbers.

Algorithm:

Gcd(a,b) = Gcd(b, a mod b), where a>=b and

Gcd(a,0) = a

Say we want to find the GCD of 72 and 105. 105 mod 72 = 33, so GCD(72,105) = GCD(33,72) 72 mod 33 = 6, so GCD(33,72) = GCD(6,33) 33 mod 6 = 3 so GCD(6,33) = GCD(3,6) 6 mod 3 = 0 so GCD(3,6) = GCD(0,3) = 3. So the GCD of 72 and 105 is 3.