An integer is a perfect number if and only if it is equal to the sum of all of its divisors except itself. For example, $28$ is a perfect number since $28 = 1 + 2 + 4 + 7 + 14$.  

Let $n!$ denote the product $1 \cdot 2 \cdot 3 \cdot \ldots \cdot n$, where $n$ is a positive integer. An integer is a factorial if and only if it is equal to $n!$ for some positive integer $n$. For example, $24$ is a factorial number since $24 = 4! = 1 \cdot 2 \cdot 3 \cdot 4$.  

Find all perfect numbers greater than $1$ that are also factorials.

Let's think step by step and output the final answer within \boxed{}.
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