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Greatest Common Factor Calculator

Please provide numbers separated by a comma "," and click the "Calculate" button to find the GCF.

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What is the Greatest Common Factor (GCF)?

In mathematics, the greatest common factor (GCF), also known as the greatest common divisor, of two (or more) non-zero integers a and b, is the largest positive integer by which both integers can be divided. It is commonly denoted as GCF(a, b). For example, GCF(32, 256) = 32.

Prime Factorization Method

There are multiple ways to find the greatest common factor of given integers. One of these involves computing the prime factorizations of each integer, determining which factors they have in common, and multiplying these factors to find the GCD. Refer to the example below.

EX: GCF(16, 88, 104)
16 = 2 × 2 × 2 × 2
88 = 2 × 2 × 2 × 11
104 = 2 × 2 × 2 × 13
GCF(16, 88, 104) = 2 × 2 × 2 = 8

Prime factorization is only efficient for smaller integer values. Larger values would make the prime factorization of each and the determination of the common factors, far more tedious.

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