# How do you find the greatest common factor of 35n^2m, 21m^2n?

Dec 1, 2016

The GCF is $7 m n$.

#### Explanation:

Find the greatest common factor (GCF) of $35 {n}^{2} m$ and $21 {m}^{2} n$.

First find the GCF, or the largest number that goes into both, of $35$ and $21$.

$35$ has factors $1 , 5 , 7 , 35$.

$21$ has factors $1 , 3 , 7 , 21$.

The greatest (or largest) number common to both lists is $7$.

Next find the GCF of the variables.. The largest power of $m$ common to both terms is $m$. The largest power of $n$ common to both term is $n$.

Thus, the GCF is $7 m n$.