very nice problem...
If N = ap * bq * cr ...
Number of factors = (p + 1)*(q + 1)*(r + 1)....
We are given number of factors = 8
=> (p + 1)*(q + 1)*(r + 1).... = 8
So the possibilities for splitting 8 are 8, 2*4, 2*2*2
so here number could be of the format a7, a*b3, a*b*c
a7 format
The smallest odd number of this format is 37. That is not a two digit number.
a*b3 format
The smallest odd number of this format is 5*33. That is not a two digit number.
a*b*c format
The smallest odd number of this format is 3*5*7. That is not a two digit number.
So, there is no odd two digit number that has 8 factors.
