Common factor

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An integer a is a common factor of two integers b and c if it is a factor of both b and c. Take, for example, the factors of 18 and the factors of 24. The factors of 18 are 1, 2, 3, 6, 9, and 18. The factors of 24 are 1, 2, 3, 4, 6, 8, 12, and 24. The common factors of 18 and 24 are 1, 2, 3, and 6 since those are the numbers that are factors of both 18 and 24. The greatest common factor of 18 and 24 is 6 since that is the greatest number that is a factor of both 18 and 24. The greatest common factor (also called the greatest common divisor) is often abbreviated to g.c.f. (or g.c.d.).