what is the smallest positive integer n for which 136 is a factor of 8 power n

Answer 1

I interpreted this question a little differently, and I feel that a GMAT-style layout of answer choices ((A) through (E), à la PS questions) or statements (as in DS questions) might help clarify the issue. Here is how I perceived the question:

What is the smallest positive integer value of n for which 8^n has 136 as a factor? In other words, (8^n)/136 must equal some integer (or else 136 would not be considered a factor).

That is a tough question, the type that could eat up a LOT of time. But with little guidance to go on from the problem, I bit the bullet and delved into the numbers. I arrived at an answer of 15. That is,

(8^15)/136 = 258,708,618,300

Each n value lower than 15 yielded a non-integer answer--yes, I actually wrote the numbers out on my notepad. I wish I could say that I had used some sort of shortcut, but I used time instead.

Phew! I hope Jim followed the correct line of reasoning. I think my brain needs a rest. In any case, good luck with your studies.

Andrew

Answer 2

Well let's look at possibilities

8^3 = 512, which can't be a factor of 136, so neither can be any greater power of 8

8^2 = 64, which isn't a factor either.

We are left with n = 1, where 8^1 = 8 and 8 is a factor of 136 --> 8 * 17 = 136, so n=1