What is the greatest common factor of 4xy^2 and 20x^2y^4 4xy 4xy^2 24xy 24xy^2

To find the greatest common factor (GCF) of $4xy^{2}$ and $20x^{2}y^{4}$, we need to find the highest power of each variable that divides both terms.<br /><br />Step 1: Find the GCF of the coefficients.<br />The GCF of 4 and 20 is 4.<br /><br />Step 2: Find the GCF of the variables.<br />For the variable x, the lowest power is 1 (in $4xy^{2}$) and the highest power is 2 (in $20x^{2}y^{4}$). Therefore, the GCF for x is $x^{1}$ or simply x.<br /><br />For the variable y, the lowest power is 2 (in $4xy^{2}$) and the highest power is 4 (in $20x^{2}y^{4}$). Therefore, the GCF for y is $y^{2}$.<br /><br />Step 3: Combine the GCFs of the coefficients and variables.<br />The GCF of $4xy^{2}$ and $20x^{2}y^{4}$ is $4xy^{2}$.<br /><br />Therefore, the correct answer is $4xy^{2}$.