Find the greatest common fact 2j^2,8j Write your answer as a constan square

To find the greatest common factor (GCF) of \(2j^2\) and \(8j\), we need to follow these steps:<br /><br />1. **Factorize each term:**<br /> - \(2j^2 = 2 \cdot j \cdot j\)<br /> - \(8j = 2 \cdot 2 \cdot 2 \cdot j\)<br /><br />2. **Identify the common factors:**<br /> - The common factors between \(2j^2\) and \(8j\) are \(2\) and \(j\).<br /><br />3. **Choose the lowest power of the common factors:**<br /> - The lowest power of \(2\) in both factorizations is \(2^1\).<br /> - The lowest power of \(j\) in both factorizations is \(j^1\).<br /><br />4. **Multiply the common factors together:**<br /> - GCF = \(2^1 \cdot j^1 = 2 \cdot j = 2j\)<br /><br />Therefore, the greatest common factor of \(2j^2\) and \(8j\) is \(2j\).<br /><br />So, the answer is:<br />\[ \boxed{2j} \]