factors

Question

how many two digit odd numbers are there with 8 factors?

Comments

NO odd 2 digit number with 8 factors.

Answer 1

very nice problem... 

If N = a^p * b^q * c^r ... 
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.