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

To find the GCF of the terms \(3xy\), \(5x^3y\), and \(7x^2\), we start by identifying the coefficients and the variable parts. The coefficients are 3, 5, and 7. The GCF of these numbers is 1, since they do not share any common factor greater than 1. Next, we look at the variables: - For \(x\), the smallest exponent is 1 (from \(3xy\)). - For \(y\), the smallest exponent is also 1 (from both \(3xy\) and \(5x^3y\)). Putting it all together, the GCF of the three terms is: \[ 1 \cdot x^1 \cdot y^1 = xy. \] Therefore, the GCF of \(3xy\), \(5x^3y\), and \(7x^2\) is \(xy\).