What is the greatest common factor of -15x^2y-10xy^3+5xy^4 5xy 5x^2y^4 5xy^2 xy

To find the greatest common factor (GCF) of the given expression \(-15x^{2}y-10xy^{3}+5xy^{4}\), we need to identify the highest power of each variable that appears in each term.<br /><br />Let's break down each term:<br />- \(-15x^{2}y\) has factors \(5\), \(x^2\), and \(y\).<br />- \(-10xy^{3}\) has factors \(5\), \(x\), and \(y^3\).<br />- \(5xy^{4}\) has factors \(5\), \(x\), and \(y^4\).<br /><br />The common factors among all three terms are:<br />- The number \(5\)<br />- The variable \(x\)<br />- The variable \(y\)<br /><br />Now, we take the lowest power of each common factor:<br />- The lowest power of \(5\) is \(5\).<br />- The lowest power of \(x\) is \(x\).<br />- The lowest power of \(y\) is \(y\).<br /><br />Therefore, the GCF is \(5xy\).<br /><br />So, the correct answer is:<br />\[ \boxed{5xy} \]