Find Smallest Number For Number of Factors
I would like to know how you would fine the smallest ordinary number with exactly a certain number of factors given, for example:
The number of factors is 6
The smallest number with 6 factors is 12
So the question is really:
The number of factors is n
The smallest number with n factors is X
How do you find X?
Please feel free to use an example because I think doing it all in algebra will be unreasonably difficult
Re: Smallest number with given number of factors
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.