If the product of the integers, w, x, y, and y is 770, and

1 < w < x < y < z, what is the value of w + z?

1. The book tells me to find the prime factorization of 770.

I found that to be 2 * 5 * 7 * 11.

2. The book tells me to let w = 2, x = 5, y = 7, and z = 11.

Thus, 1 < 2 < 5 < 7 < 11 is a true statement.

3. From step 2, I figured out that w + z = 2 + 11 or 13.

Question:

What information in this problem indicates that prime factorization is needed as step one?