Find the GCF (greatest common factor) of the following terms.
\[
\left\{8 x y^{2}, 24 x y, 40\right\}
\]

Step 1 ：Find the GCF (greatest common factor) of the following terms: \(\{8 x y^{2}, 24 x y, 40\}\).

Step 2 ：The GCF of a set of numbers is the largest number that divides evenly into all of the numbers. To find the GCF of these terms, we need to find the GCF of their coefficients and the GCF of their variables.

Step 3 ：The coefficients are 8, 24, and 40. The variables are \(x\), \(y^2\), and \(y\).

Step 4 ：The GCF of the coefficients can be found by listing the factors of each number and finding the largest number that appears in all lists.

Step 5 ：The GCF of the variables can be found by taking the lowest power of each variable that appears in all terms.

Step 6 ：The GCF of the coefficients is 8. The GCF of the variables is \(x^0y^0\), which is just 1. Therefore, the GCF of the terms is \(8 \times 1 = 8\).

Step 7 ：Final Answer: The GCF of the terms \(\{8 x y^{2}, 24 x y, 40\}\) is \(\boxed{8}\).