2 x 3 x 5 = 30
How about: 210
30
3
2*3*5 = 30
Seven distinct factors.
16 if the prime factors don't have to be distinct. 210 if they do.
Distinct would mean they are all different, so take the 3 lowest primes and multiply them: 2*3*5 = 30
The smallest prime factors are 2,3,5,7 thus the smallest number would be the product of these will be 210
240 is the smallest number with twenty factors.
11
24edit: nonethe smallest number with 12 distinct factors would be2*3*5*7*11*13*17*19*23*29*31*37>>100
Every number has factors. They are endless.