Thanks Guest,
CU's question,
why does doing 2^6 * 3 give 14 positive divisors?
Just count them
1,2,4,8,16,32 64 that is all the factors of 2^6
so that is 7 factor
then
1,3 are the only factors of 3 and you already have 1
so that is another factor, making 8 factors,
Then
2*3=6
4*3=12
8*3=24
16*3=48
32*3=96
64*3=192
So that is another 6
Making 8+6=14 factors altogether.
So 2^6*3 defiitely has 14 factors but I am not necessarily convinced that it is the smallest number with 14 factors.