question_answer

A number n is divisible by only two primes. Also twice of the number is a perfect square while thrice of the number is a perfect cube. The number of factors of least possible value of n is

A)  6                                

B)  8            

C)  10                  

D)  12

Correct Answer: D

Solution :

\[\frac{144}{2}=72\] \[72\times 3=216\] No. is 72 \[{{2}^{3}}\times {{3}^{2}}\] \[\therefore \]No. of factor \[\Rightarrow \text{ }4\times 3=12\] No. of factor\[=12\]