Let N be any natural number and , where are prime numbers and are natural numbers.

Then number of factors of N is given by

You are given number of factors say k.First step would be to factorize k.That is write k as .

Once you have found out such that , your x would be

Main thing here is that you can multiple possibilities for and you have to optimize for that.

Example:Given k=12,find x.

k=3*2*2 . Corresponding x = =60

k=6*2 . Corresponding x = = 96

k=4*3 . Corresponding x = = 72

So minimum x would be 60.