Find the GCF of the following terms. \( 52 x y^{3}, 65 x^{2} y^{2},-13 x^{2} y \) The GCF is

To find the GCF of the given terms \( 52xy^{3}, 65x^{2}y^{2}, -13x^{2}y \), we start by identifying the GCF of the numerical coefficients: 52, 65, and -13. The GCF of these numbers is 13. Next, for the variables, we take the lowest power for each common variable: for \( x \), the lowest power is \( x \) (from \( xy^{3} \)), and for \( y \), it is \( y \) (from \( -13x^{2}y \)). Putting it all together, the GCF is \( 13xy \). To check if our GCF is correct, we can divide each term by \( 13xy \) and see if we get whole numbers. Dividing \( 52xy^{3} \) gives \( 4y^{2} \); \( 65x^{2}y^{2} \) gives \( 5x^{2}y \); and dividing \( -13x^{2}y \) gives \( -x \). Since all results are integers, \( 13xy \) is indeed the greatest common factor!