TITLE: How can I unfactorilize number?
QUESTION [6 upvotes]: Consider the equation
$x! = y$
Say we know $y$ and were trying to find $x$:
What method could I use to get $x$ (e.g. a closed formula)?

REPLY [19 votes]: Are you insisting that solutions be integer? If so, start by dividing $y$ by $2$, then the quotient by $3$, then the quotient of that by $4$, and so on. If you reach $1$, there is a solution and the last number you divided by is $x$. If you reach smaller than $1$ before reaching $1$, there is no integer solution.