Find the GCF (greatest common factor) of the following terms. \[ \left\{3 x y, 5 x^{3} y, 7 x^{2}\right\} \]

Step 1 ：Find the GCF (greatest common factor) of the following terms: \(\{3 x y, 5 x^{3} y, 7 x^{2}\}\).

Step 2 ：The GCF of a set of terms is the product of the smallest power of each common factor in these terms.

Step 3 ：In this case, the common factors are x and y.

Step 4 ：The smallest power of x in these terms is 1 (in the term 3xy) and the smallest power of y is also 1 (in the term 7x^2).

Step 5 ：Therefore, the GCF is \(x^1 * y^1 = xy\).

Step 6 ：Final Answer: The GCF of the terms is \(\boxed{xy}\).