All numbers have factors. Some numbers have some of the same factors as other numbers. These are known as common factors. If you compare the lists of factors, you will see which ones are common.
Example: 30 and 42
1, 2, 3, 5, 6, 10, 15, 30
1, 2, 3, 6, 7, 14, 21, 42
The common factors are 1, 2, 3, 6
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One way is to list them.
The factors of 30 are:
1, 2, 3, 5, 6, 10, 15, 30
The factors of 42 are:
1, 2, 3, 6, 7, 14, 21, 42
The common factors are:
1, 2, 3, 6
Example: 30 and 42
Factor them.
2 x 3 x 5 = 30
2 x 3 x 7 = 42
Select the common factors.
2 x 3 = 6, the GCF
Factor two numbers. Example: 30 and 42
2 x 3 x 5 = 30
2 x 3 x 7 = 42
Select the common factors.
2 x 3 = 6, the GCF
If you construct them correctly, factor trees always work to determine the prime factorization of a number. Once you compare the prime factorizations of two or more numbers, it is relatively easy to find the greatest common factor of them from there.
Most Common Factor, Greatest Common Factor, Highest Common Factor... all the same thing.
There is no "common factor" of 350, to have a common factor you must have more than one number, so there is no common factor of 350.
2 is a common factor.
The least common factor is 1 but the highest common factor is 4