The greatest common factor (or greatest common divisor) of a set of natural numbers is the largest natural number that divides each member of the set evenly (with no remainder). For example, 6 is the greatest common factor of the set {12, 18, 30} because 12 ÷ 6 = 2, 18 ÷ 6 = 3, and 30 ÷ 6 = 5.

Similarly, the greatest common factor of a set of polynomials is the polynomial of highest degree that divides each member of th set with no remainder. For example, 3(x+2)³(x-4)², 12(x+2)⁴(x-4)³(x2+x+5), and 6(x+2)²(x-4) have 3(x+2)²(x-4) for the highest common factor.