Which subset of \( A \) has a GCF of the elements that is \( 2 x \) ? A. \( \{2 x, 4 x, 12 x y\} \) B. \( \{2 x, 4 x, 5 x y, 7 x, 12 x y, 13 x, 15 x\} \) C. \( \{4 x, 12 x y\} \) D. \( \{2 x, 5 x y, 12 x y\} \) Video Textbook Get more heln

To find the subset of \( A \) with a greatest common factor (GCF) of \( 2x \), we can break down each option to identify which has \( 2x \) as the highest common factor. For option A, the GCF is \( 2x \). Option B also has \( 2x \) as the GCF when considering all terms. Option C has a GCF of \( 4x \), and option D has a GCF of \( x \) as it does not contain \( 2 \) as a factor. Therefore, the correct subsets with a GCF of \( 2x \) are options A and B! Did you know that using the prime factorization of each term can help visualize how to find the GCF more easily? For example, \( 4x \) breaks down to \( 2^2 \cdot x \), while \( 2x \) is simply \( 2 \cdot x \). This method can clarify your calculations, especially for more complex problems down the road! In real-world applications, GCF concepts play a pivotal role in simplifying fractions, optimizing resource sharing, and even in programming for efficient data organization. Understanding how to find the GCF can streamline tasks in various fields, ensuring you use only the necessary elements of your data!