SOLUTION: what is the least positive integer that has exactly 9 factors?

Question 938445: what is the least positive integer that has exactly 9 factors?
Found 2 solutions by Fombitz, KMST:
Answer by Fombitz(32388) (Show Source): You can put this solution on YOUR website!
I'm assuming you mean unique prime factors (?).

If they don't have to be unique,

If they don't have to be prime,

Answer by KMST(5328) (Show Source): You can put this solution on YOUR website!
A number has more or less factors depending on its prime factorization.
If the prime factorization is

those prime factors can be arranged into products of the form

with , , etc
to form all factors of
from to
.
The number of possible products is
,
with as many such brackets as prime factors,
(multiplied together if there is more than one),
and each bracket being 2 or more.
In this case, is the number of factors,
meaning that there are just 2 prime factors,
both with 2 as an exponent:
with .
The smallest we can make with that formula is
.
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