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A single number cannot have a common factor. The word "common" implies that the factor is common to two or more numbers.

A systematic way of finding a common factor of two or more numbers is first to find the prime factorisation of each of the numbers. The common factors are any primes that appear in each and every on of these factorisations, as well as their products.

For example, suppose you want common factors of 24, 36 and 60

12 = 2*2*2*3

18 = 2*2*3*3

30 = 2*2*3*5

The factors common to all three are 2, another 2 and 3.

So the common factors are 1, 2, 3, 2*2 = 4, 2*3 = 6 and 2*2*3 = 12.

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9y ago

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