Chapter 6 - Factoring, Solving Equations, and Problem Solving - 6.1 - Factoring by Using the Distributive Property - Problem Set 6.1 - Page 242: 5

$14ab^2$

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 both expressions. The greatest value that goes both into $42ab^3$ and $70a^2b^2$is $14ab^2$, so this is the greatest common factor.