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

Dec 11, 2016

The GCF of $25$ and $35$ is $5$.

#### Explanation:

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

$25 = {5}^{2}$
$35 = 5 \cdot 7$

Now, we can find all the factors $25$ and $35$ have in common. We see that $25$ and $35$ both have a $5$, but not ${5}^{2}$ because $35$ only has one $5$.

$35$ also has a $7$, but that is not in the prime factorization of $25$, so we do not include it. Since there is only one common factor which is 5, that is our "greatest common factor".