24
edit: none
the smallest number with 12 distinct factors would be
2*3*5*7*11*13*17*19*23*29*31*37>>100
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11
4, 9, 25, 49
6 (1,2,3,6) 10 (1,2,5,10) and 15 (1,3,5,15).
The numbers less than 100 with exactly 6 factors are of the form a2b where a and b are different primes. 12, 18, 20, 28, 44, 45, 50, 52, 63, 68, 75, 76, 92 and 99.
yes. for all positive, distinct numbers greater than 0