What is the greatest common factor (GCF) of 25 and 35?

1 Answer
Dec 11, 2016

The GCF of 2525 and 3535 is 55.

Explanation:

One way to find the GCF is to find the prime factorization of each number. So,

25 = 5^225=52
35 = 5*735=57

Now, we can find all the factors 2525 and 3535 have in common. We see that 2525 and 3535 both have a 55, but not 5^252 because 3535 only has one 55.

3535 also has a 77, but that is not in the prime factorization of 2525, so we do not include it. Since there is only one common factor which is 5, that is our "greatest common factor".