Find the smallest positive integer which have the same number of positive factors as 2015 ?

The prime factors of 2015 are: 
5 x 13 x 31 

We can choose to include or exclude each of these prime factors and that will form 2 x 2 x 2 = 8 factors, namely: 
1, 5, 13, 31, 65, 155, 403, 2015 

We want to form another number that has exactly 8 factors. So we need 3 primes with one that overlaps with 2015. The obvious choice is 2 x 3 x 5 

 
30 is the smallest positive number that also has 8 divisors (namely, 1, 2, 3, 5, 6, 10, 15, 30)