Factors that are shared by two or more numbers are called common factors. The greatest of these common factors is called the greatest common factor (GCF). Consider, for example, the factors of 4 and 8. Factors of4: & 1, 2, 4 Factors of8: & 1, 2, 4,8 The common factors of 4 and 8 are 1, 2, and 4. The GCF(4,8)= 4. The GCF can also be determined by multiplying the prime factors shared in the prime factorization of the numbers in question.

Common factors can be extended to expressions with variable terms. For example, consider the expressions 4x and 2x. Factors of4x: & 1,2,4,x, 2x,4x Factors of2x: & 1,2,x, 2x The GCF(4x,2x)= 2x. It should be noted that the greatest common factor is also called the greatest common divisor because a factor of a number divides that number evenly.