Find the greatest common factor. \( 9 \mathrm{~m}^{3}, 6 \mathrm{~m}^{3} \) Write your answer as a constant times a product of single variables raised to exnonents.

To find the greatest common factor (GCF) of \(9 \mathrm{~m}^{3}\) and \(6 \mathrm{~m}^{3}\), we start by factoring the constants and the variable parts separately. The factors of \(9\) are \(1, 3, 9\), and the factors of \(6\) are \(1, 2, 3, 6\). The greatest common factor of the constants \(9\) and \(6\) is \(3\). For the variable part, both have \(m^{3}\), so we take the exponent of \(m\) as is since they are equal. Thus, the GCF is \(3 \mathrm{~m}^{3}\). So, your answer is \(3 \mathrm{~m}^{3}\). Did you know that finding the GCF is a key step in simplifying fractions? When you break down numbers to their GCF, it becomes not just a number, but a gateway to understanding relationships between multiple values! To explore more about the importance of GCF, check out resources like math tutorial websites or algebra textbooks that emphasize factorization techniques. They'll guide you through not just GCF, but also learning how to use it effectively in problem-solving!