Find the GCF of \( 108 x^{5} y^{3} \) and \( 96 x^{7} \), \( 108 x^{5} y^{3} \) \( 96 x^{7} y^{2} \) GCF \( = \)

To find the GCF of \( 108 x^{5} y^{3} \) and \( 96 x^{7} \), we first look at the numerical coefficients. The prime factorization of 108 is \( 2^2 \times 3^3 \), and for 96, it's \( 2^5 \times 3^1 \). The GCF for the coefficients is \( 2^2 \times 3^1 = 12 \). Next, for the variables, we take the lowest power of each variable present in both terms. The GCF for \( x^{5} \) and \( x^{7} \) is \( x^{5} \), and since \( y^{3} \) isn’t in the second term, we don’t include \( y \). Combining these gives us the GCF: \[ \text{GCF} = 12 x^{5} \] --- Now, for the second pair \( 108 x^{5} y^{3} \) and \( 96 x^{7} y^{2} \), we follow a similar approach. The numerical coefficients remain the same: the GCF is \( 12 \), as derived earlier. For the variables, we take the lowest powers: for \( x^{5} \) and \( x^{7} \) it's still \( x^{5} \), and for \( y^{3} \) and \( y^{2} \), it’s \( y^{2} \). Thus, the GCF is: \[ \text{GCF} = 12 x^{5} y^{2} \]