Find the greatest common factor of these two expressions. 24v^7w^2 and 14u^6v^4w^5 square

## Step 1<br />The greatest common factor (GCF) of two or more numbers or algebraic expressions is the largest number or expression that divides evenly into each of them. In this case, we are asked to find the GCF of \(24v^{7}w^{2}\) and \(14u^{6}v^{4}w^{5}\).<br /><br />## Step 2<br />First, we need to break down each term into its prime factors. The prime factorization of 24 is \(2^3 * 3\), and the prime factorization of 14 is \(2 * 7\). <br /><br />## Step 3<br />Next, we look at the variables. The variable \(v\) appears in both terms, with powers of 7 and 4. The GCF of these powers is \(v^4\), because 4 is the smaller of the two powers. <br /><br />## Step 4<br />Similarly, the variable \(w\) appears in both terms, with powers of 2 and 5. The GCF of these powers is \(w^2\), because 2 is the smaller of the two powers. <br /><br />## Step 5<br />Therefore, the GCF of \(24v^{7}w^{2}\) and \(14u^{6}v^{4}w^{5}\) is \(2 * v^4 * w^2\), which simplifies to \(2v^4w^2\).