def greatest_common_divisor(a: int, b: int) -> int:
    """
    Euclid's Lemma :  d divides a and b, if and only if d divides a-b and b

    Euclid's Algorithm

    >>> greatest_common_divisor(7,5)
    1

    Note : In number theory, two integers a and b are said to be relatively prime,
           mutually prime, or co-prime if the only positive integer (factor) that
           divides both of them is 1  i.e., gcd(a,b) = 1.

    >>> greatest_common_divisor(121, 11)
    11

    """
    if a < b:
        a, b = b, a

    while a % b != 0:
        a, b = b, a % b

    return b