#### Answer

$5mn$

#### Work Step by Step

The greatest common factor of a group of terms is the greatest factor that evenly divides into all terms in the group.
In this case, $5mn$ is the greatest common factor, because it is the largest factor that divides evenly into all 3 terms.
$10m^{2}n^{2}\div5mn=2mn$
$25mn^{3}\div5mn=5n^{2}$
$50m^{2}n\div5mn=10m$