Greatest Common Factor
Greatest Common Factor
The greatest common factor (or greatest common divisor) of a set of natural numbers (positive integers) is the largest natural number that divides each member of the set evenly, that is, with no remainder. For example, 6 is the greatest common factor of 1246, 1846, and 3046 because 1246 = 2, 1846 = 3, and 3046 = 5, and no larger natural number divides all three of these numbers evenly.
Similarity, 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. Polynomials is the polynomial of highest degree that divides each member of the 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.