Find the GCF: a) \( 15 m^{3} n^{6} \) and \( 45 m^{4} n^{2} \)

To find the GCF (Greatest Common Factor) of \( 15 m^{3} n^{6} \) and \( 45 m^{4} n^{2} \), we start with the numerical coefficients. The GCF of 15 and 45 is 15. Next, for the variable \( m \), we take the lowest exponent, which is \( m^{3} \). For \( n \), the lowest exponent is \( n^{2} \). Putting it all together, the GCF is \( 15 m^{3} n^{2} \). The GCF allows us to factor out common terms, making polynomial expressions easier to manage. For instance, if you’re simplifying equations or solving problems in algebra, finding the GCF can help break down complicated expressions into simpler parts. It’s also handy for reducing fractions! Understanding how to find the GCF can help you avoid common pitfalls in factoring. One common mistake is forgetting to compare both coefficients and exponents separately, which can lead to incorrect results. Always remember to break it down step by step to ensure accuracy!