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Concept

Greatest Common Factor

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 and
The common factors of and are and The The GCF can also be determined by multiplying the prime factors shared in the prime factorization of the numbers in question.
Prime factorization of 4: 2 * 2. Prime factorization of 8: 2 * 2 * 2. The common prime factors (2 and 2) are shown within a circle. The product of these common prime factors is 4 (2 * 2).
Common factors can be extended to expressions with variable terms. For example, consider the expressions and
The 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.