Find the greatest common factor. \[ 6 r, 9 r^{2} \]

To find the greatest common factor (GCF) of \( 6r \) and \( 9r^2 \), we can start by factoring each term. The number \( 6 \) can be factored as \( 2 \times 3 \) and \( 9 \) can be factored as \( 3 \times 3 \). Both terms share a common factor of \( 3 \). Now, considering the variable part, \( r \) in \( 6r \) is just \( r^1 \) and in \( 9r^2 \) it is \( r^2 \). The GCF of the variable is \( r^1 \) since we take the lowest power. So, combining both, the GCF is: \[ 3r. \] Now you've got \( 3r \) as the greatest common factor of \( 6r \) and \( 9r^2 \)! 🌟 Keep this GCF in mind, as it can be helpful for simplifying expressions or solving equations involving these terms. Additionally, knowing the GCF is useful in various mathematical concepts like factoring polynomials and reducing fractions. It’s a foundational skill that supports your understanding of more advanced topics, like finding least common multiples or solving Diophantine equations. So, keep practicing, and this will all become second nature! 🧠✨