24x^2 = 2 * 2 * 2 * 3 * x * x
40x^3 = 2 * 2 * 2 * 5 * x * x * x
The GCF is made of the factors that appear in both 24x^2 and 40x^3. Both of those have three 2's and two x's, so the GCF is 2 * 2 * 2 * x * x = 8x^2.
Answer: The GCF of 24x^2 and 40x^3 is 8x^2.