If tuvw = 108, and t, u, v, and w are all positive integers

gmattesttaker2 wrote: If tuvw = 108, and t, u, v, and w are all positive integers such that t > u > v > w, what is the greatest possible value for t - w?

A) 1
B) 16
C) 17
D) 18
E) 19

To maximize the value of t - w, we must MAXIMIZE t and MINIMIZE w

First find the prime factorization of 108.
108 = (2)(2)(3)(3)(3)

We can also add a 1 to this product to get: 108 = (1)(2)(2)(3)(3)(3)
So, the smallest value in our product is 1.
So, w = 1

The next smallest value in our product is 2
So, v = 2

The next smallest value in our product is 3
So, u = 3

Now that we've MINIMIZED the values of w, v and u, we have MAXIMIZED the value of t
If w = 1, v = 2 and u = 3, then t = 18

So, t - w = 18 - 1 = [spoiler]17 = C[/spoiler]

Cheers,
Brent