100 = 2 x 2 x 5 x 5
120 = 2 x 2 x 2 x 3 x 5
The common factors are 2, 2, and 5.
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The prime factors of 100 are 2, 2, 5, and 5. The prime factors of 120 are 2, 2, 2, 3, and 5. The prime factors of 180 are 2, 2, 3, 3, and 5. The prime factors that all three numbers have in common are 2, 2, and 5. Therefore, the greatest common factor is 2 x 2 x 5 = 20.
There is neither a greatest common factor nor common factors of a single number, such as 120, because there cannot be any form of common factor without two or more numbers to compare. Common factors are factors that the numbers being compared have in common. The greatest common factor is the largest factor that all the numbers being compared have in common. Thus, since there are not two or more numbers to compare, there are neither common factors nor a greatest common factor. The factors of 120 are 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, and 120. The prime factors of 120 are 2, 2, 2, 3, and 5. Examples: The common factors of 16 and 120 are 1, 2, 4, and 8; the greatest common factor is 8. The common factors of 36 and 120 are 1, 2, 3, 4, 6 and 12; the greatest common factor is 12. The common factors of 96 and 120 are 1, 2, 3, 4, 6, 8, 12, and 24; the greatest common factor is 24.
49 and 100 share no common factors aside from 1.
Since 100 is a factor of 200, all of its factors are common.
1 and 5 are their only common factors.