Problem Solving

Hi Vincen,

For 130/X to be an integer, X must be a factor of 130. There are a couple of different ways to determine all of the different factors of 130: you can 'brute force' the list or use prime-factorization.

If you prime-factor 130, you'll get...
(2)(65)
(2)(5)(13)

Thus, the factors of 130 are:
1
2
5
13
(2)(5) = 10
(2)(13) = 26
(5)(13) = 65
(2)(5)(13) = 130

Total = 8 (you should also notice that this is the largest possible answer among the 5 choices, so there's no way that you 'missed' any of them).

Final Answer: A

GMAT assassins aren't born, they're made,
Rich

Vincen wrote:For how many positive integer x is 130/x an integer?

(A) 8
(B) 7
(C) 6
(D) 5
(E) 3

If x is a positive integer and 130/x is an integer, then x must be a factor of 130. Thus, we need to determine the number of factors of 130. To determine the number of factors, we break down 130 into primes and add 1 to the exponent of each unique prime, and then multiply. Thus:

130 = 10 x 13 = 2^1 x 5^1 x 13^1

Thus, 130 has (1 + 1)(1 + 1)(1 + 1) = 2 x 2 x 2 = 8 total factors.

Answer: A