The only prime factors of a number are 5 and 17.

[ArjunJ720]

Hi,

I am looking at the Foundations of GMAT Math 5th edition book. In Chapter 2 drill set 8 (page 89) I am confused with this question:

31. The only prime factors of a number are 5 and 17. What is the number and what are all its factors?

I said it cannot be determined but the book's answer is to the number 85 (17x5). Please explain why a number like 17 squared x 5 squared (or 17 cubed x 5 cubed) cannot work.

Thanks.

[RonPurewal]

You're right, of course; the number can contain any nonzero power of 5 and any nonzero power of 17.

My only guess is that the problem was originally written with some sort of additional restriction (to rule out multiple 5's or multiple 17's). But, about the problem as written, you're correct.

Thanks.