# 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.

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**Greatest Common Factor**