Chapter 6 - Factoring, Solving Equations, and Problem Solving - 6.1 - Factoring by Using the Distributive Property - Problem Set 6.1 - Page 242: 8

$12xy$

When we are looking for the greatest common factor, we are trying to find the greatest expression that can be multiplied by a whole number to get all three expressions. The greatest value that goes into $72xy$, $36x^2y$, and $84xy^2$ is $12xy$, so this is the greatest common factor.