That's just as meaningless a question as asking "what is the biggest number?" Just as there is no biggest number (you can always get bigger numbers by adding 1), there is no odd number with the most factors. You could multiply any odd number by 3, and get an odd number with another factor of 3.
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Square numbers have an odd number of factors.
Perfect squares are numbers with an odd number of factors.
Square numbers have an odd number of factors, but beyond that, any odd number can be a factor.
All square numbers have an odd number of factors.
I guess it would be 45,63,75,99 they each have 6 factors