Data Sufficiency

If N is an integer, then N is divisible by how many positive integers?

(1) N is the product of 2 different prime numbers
(2) N and 2 ^3 are each divisible by the same number pf positive integers.

the OA is D. But I got B because

in #1 N could be 17 (divisible by only 2 numbers 1 and 17) or it could be 10 (divisible by 5, 2, 10, 1) therefore since both 17 and 10 satisfy the condition and 17 is divisible by 2 positive integers and 10 is divisible by 4, its insufficient. Can someone explain why I'm wrong?

Perhaps one isn't a prime number?

Hi

n= a*b (where and b are prime nos)...
this implies cannot be 17 as stated by you since since 1 is not prime.

From 1 n will have factors n,1,a,b.

Hope this helps....

PS if N can be factorised into prime nos u van always find the no. of factors using this formula

N= (a^p)*(b^q).....(a and b are prime)
no of factors = (p+1)*(q+1).....