# Greatest Common Factor

### set remainder divides example

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 because 1246 = 2, 1846 = 3, and 3046 = 5.

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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