Find the greatest common factor of these two expressions.

16w^3x^8v^4
and
28x^2v^7

4x^2v^4

To find the greatest common factor of two expressions, we need to determine the highest power of each variable that appears in both expressions. Let's break down both expressions and identify the common factors for each variable.

Expression 1: 16w^3x^8v^4
Expression 2: 28x^2v^7

Step 1: Identify the common factors for each variable individually.

For the variable w:
Expression 1: It has w^3.
Expression 2: It doesn't have w.

For the variable x:
Expression 1: It has x^8.
Expression 2: It has x^2.

For the variable v:
Expression 1: It has v^4.
Expression 2: It has v^7.

Step 2: Identify the highest power of each common factor.

For w, we have w^3 in expression 1 and none in expression 2. Therefore, the highest power of w is w^3.

For x, we have x^8 in expression 1 and x^2 in expression 2. Therefore, the highest power of x is x^2.

For v, we have v^4 in expression 1 and v^7 in expression 2. Therefore, the highest power of v is v^4.

Step 3: Combine the highest powers of each common factor.

The greatest common factor is the product of the highest powers of the common factors. In this case, we have w^3, x^2, and v^4 as the highest powers for the common factors. Therefore, the greatest common factor of the two expressions is:

GCF = w^3 * x^2 * v^4

So, the greatest common factor of 16w^3x^8v^4 and 28x^2v^7 is w^3x^2v^4.