Find the greatest common factor. 2y^2,2y^3 Write your answer as a constant times a product o square

To find the greatest common factor (GCF) of \(2y^2\) and \(2y^3\), we need to identify the highest power of each common factor in both terms.<br /><br />1. **Identify the common factors:**<br /> - Both terms have a common factor of \(2\).<br /> - Both terms have a common factor of \(y\).<br /><br />2. **Determine the lowest powers of the common factors:**<br /> - The lowest power of \(2\) in both terms is \(2^1\).<br /> - The lowest power of \(y\) in both terms is \(y^2\).<br /><br />3. **Multiply the lowest powers of the common factors:**<br /> - The GCF is \(2^1 \cdot y^2\).<br /><br />Therefore, the greatest common factor of \(2y^2\) and \(2y^3\) is:<br />\[ 2y^2 \]<br /><br />So, the answer is:<br />\[ 2y^2 \]