Question

How many two digit odd numbers are there with 10 factors?

• A. 1
• B. 2
• C. 3
• D. 4
• E. None of these

Answer 1

The correct option is E None of these

10 factors implies that the number can be of the form

1) $a^9$ ( Least odd number will be $3^9$)

2) $a{b}^4$ (Least odd number will be $3^4\ast 5=405$)

Therefore, as the least number is 405, there are no two digit numbers of the specified form. The answer is 0.

If a number N can be factorized as $N=a^m\ast b^n$(a, b are the prime factors)

Then number of factors= (m+1)(n+1)