Chapter 6 - Factoring, Solving Equations, and Problem Solving - 6.1 - Factoring by Using the Distributive Property - Problem Set 6.1 - Page 242: 9

$8a^2b^2$

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 $16a^2b^2$, $40a^2b^3$, and $56a^3b^4$ is $8a^2b^2$, so this is the greatest common factor.