The largest integer or the polynomial (monomial) of highest degree that is an exact divisor or each of two or more integers or polynomials.

In mathematics, the greatest common divisor (gcd), sometimes known as the greatest common factor (gcf) or highest common factor (hcf), of two non-zero integers, is the largest positive integer that divides both numbers without remainder. Some authors emphasize that "greatest" is not so much a measure of magnitude as a label for the fact that any other common divisor of two numbers divides their gcd. These authors also do not require the gcd to be positive, so that there are two gcds a and b, with a = −b.