Finding Total Number of Factors (-ve Factor inclusion)

GRE Quant Problem Solving
1

Can anyone please help me with the formula for finding the total no. of factors of an integer?

The usual way is prime factorization; then increasing the exponent of each prime factor by one; and multiplying the raised numbers.

E.g:

Q. Find the no. of factors of 90?

A.

90 = 2^1 x 3^2 x 5^1

So total factors = (1+1) x (2+1) x (1+1) = 2 x 3 x 2 = 12.

I have a test prep where the solution actually doubles this answer saying that 12 are positive factors and there are as many negative factors.

So the total no. of factors should be 12 x 2 = 24.

But I researched a bit on the internet and almost everywhere they don’t double the answer, i.e. they say the answer is 12.

What is right on GRE?

2

I’ve seen ETS questions explicitly state positive factors in the question. Example: Big book, test 5, section 3 question 12. I guess if it doesn’t mention that you need to consider all type of factors.

3

Thanks for the response, but in GMAT club, I have seen people saying in GMAT universe Total factors =. Positive factors, there is an official GMAC question as well as per the forum, I was wondering whether the same is applicable to the GRE/ETS as well.

4

Yes, I think your guess is right.

The factors of a number in GRE are always POSITIVE.

P.S. If you comes across such a question that involves factors, please consider only positive.

5

Thanks for the clarification, I wish we could substantiate this with something official.
Thanks again