The greatest common divisor (GCD) of two or more integers is the largest positive integer that divides each of the integers without leaving a remainder. It is denoted by gcd(a,b), where a and b are the integers in question. The properties of GCD are as follows:

Existence: The GCD of any two integers always exists and is unique.

Commutativity: gcd(a, b) = gcd(b, a) for any integers a and b.

Associativity: gcd(a, b, c) = gcd(gcd(a, b), c) for any integers a, b, and c.

Bezout's Identity: If gcd(a, b) = d, then there exist integers x and y such that d = a * x + b * y.

Linear Combination: If gcd(a, b) = d, then any multiple of d can be written as a linear combination of a and b.

These properties make the GCD a useful tool in number theory and other related fields, as it helps to determine the highest common factor of two or more integers and reduces the complexity of calculations involving multiple integers.