Find the greatest common factor. \( 15 q^{3}, 3 q^{3}, 3 q^{4} \)

To find the greatest common factor (GCF) of the terms \( 15 q^{3}, 3 q^{3}, 3 q^{4} \), we start with the numerical coefficients. The GCF of \( 15, 3, \) and \( 3 \) is \( 3 \). Next, for the variable part, the lowest power of \( q \) that appears in all terms is \( q^{3} \). Hence, the GCF of the expressions is \( 3 q^{3} \). Remember, finding the GCF is like unearthing the treasure that’s hiding in plain sight! It’s a sweet combination of common elements that works wonders in simplifying problems in math. In real-world applications, the GCF is a handy tool! For instance, if you’re cutting pieces of fabric to the same length or dividing something into equal parts without leftovers, knowing the GCF helps ensure you've got the best division to take. Imagine trying to bake a set of cookies where portions need to be equal—using GCF ensures everyone gets the same delicious share!