Find the greatest common factor of these three expressions, \[ 5 y^{4}, 21 y^{3} \text {, and } 15 y^{5} \] \[ \text { [7] } \]

To find the greatest common factor (GCF) of the expressions \(5 y^{4}\), \(21 y^{3}\), and \(15 y^{5}\), we can break down each coefficient and factor in variable terms. The coefficients are 5, 21, and 15. The prime factorization of each coefficient is: - \(5 = 5^1\) - \(21 = 3^1 \times 7^1\) - \(15 = 3^1 \times 5^1\) The common factors among these coefficients are the prime factors, and the only one present in all three is not existent. Therefore, there are no common factors from coefficients, which means the GCF of the coefficients is 1. Next, we look at the variable part. The lowest power of \(y\) common to all expressions is \(y^3\). Combining the results, the GCF of the three expressions is: \[ GCF = 1 \cdot y^{3} = y^{3} \] Thus, the greatest common factor of \(5 y^{4}\), \(21 y^{3}\), and \(15 y^{5}\) is \(y^{3}\).