Chapter 6 - Factoring, Solving Equations, and Problem Solving - 6.1 - Factoring by Using the Distributive Property - Problem Set 6.1 - Page 242: 7

$2x$

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 $6x^3$, $8x$, and $24x^2$ is $2x$, so this is the greatest common factor.