Find the smallest positive integer that has exactly 16 positive divisors.
I kinda know how to approach this problem but I'm not sure how to answer it in a formal way.
Please help!!! Thank you in advance.
Let be the prime factorization of .
If you recall the properties of , we want:
Now, can be written as a product of integers in only 5 ways:
So our possibilities:
Since we want the smallest integer, we consider the smallest primes in the factorization of . So this narrows our list down to: