We’re also going to talk about the GCF (or greatest common factor).

The GFC is the product of the prime factors that two (or more) terms have in common.

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Greatest Common Factor.

Let a and b be natural numbers.

The common factor of a and b are those natural numbers that divide both a and b. The greatest common factor now is the largest of these common factors.

EXAMPLE 1. Find the greatest common factor of 18 & 24.

Solution. First list the factors of each number, the numbers that divide each single number with zero remainders.

Factors of 18: 1; 2; 3; 6; 9; and 18

Factors of 24: 1; 2; 3; 4; 6; 8; 12; and 24

The common factors here are:1; 2; 3; and 6

The GCF (the greatest common factor) is the largest of the common factors. That is 6.

Greatest Common Factor (GFC) = 6.

That is, the largest number that divides both 18 and 24 is the number 6.

So we must find the GCF (greatest common) factor of 12 and 18

Factors of 12 are: 1; 2; 3; 4; 6; and 12

Factors of 18 are: 1; 2; 3; 6; 9; and 18

The common factors here are: 1; 2; 3; and 6

Greatest Common Factor (GFC) = 6