Definition: Greatest common divisor Let \(a\) and \(b\) be integers, not both zero. The largest integer \(d\) such that \(d\) is a factor of \(a\) and \(d\) is a factor of \(b\) is called the greatest common divisor of \(a\) and \(b\) and is denoted by \(gcd(~(a, b)~)\).