Find the greatest common factor. 9p, 6p^3 Write your answer as a constant times a produc square

To find the greatest common factor (GCF) of \(9p\) and \(6p^3\), we need to follow these steps:<br /><br />1. **Factorize each term:**<br /> - \(9p = 3^2 \cdot p\)<br /> - \(6p^3 = 2 \cdot 3 \cdot p^3\)<br /><br />2. **Identify the common factors:**<br /> - The common prime factors between \(9p\) and \(6p^3\) are \(3\) and \(p\).<br /><br />3. **Choose the lowest power of each common factor:**<br /> - For \(3\), the lowest power is \(3^1\).<br /> - For \(p\), the lowest power is \(p^1\).<br /><br />4. **Multiply these together to get the GCF:**<br /> - GCF = \(3^1 \cdot p^1 = 3p\)<br /><br />So, the greatest common factor of \(9p\) and \(6p^3\) is \(3p\).<br /><br />Therefore, the answer is:<br />\[ 3p \]