gcd(0, v) = v, because everything divides zero, and v is the largest number that divides v. Similarly, gcd(u, 0) = u. gcd(2u, 2v) = 2·gcd(u, v) gcd(2u, v) = gcd(u, v), if v is odd (2 is not a common divisor). Similarly, gcd(u, 2v) = gcd(u, v) if u is odd. gcd(u, v) = gcd(|u − v|, min(u, v)), if u and v are both odd.