Given that $\displaystyle {{\left((3!)!\right)!}\over{3!}}= k\cdot
n!$, where $k$ and $n$ are positive integers and $n$ is as large as possible, find $k+n$.
<|im_start|>system
You are a helpful assistant.<|im_end|>
<|im_start|>user
Given that $\displaystyle {{\left((3!)!\right)!}\over{3!}}= k\cdot
n!$, where $k$ and $n$ are positive integers and $n$ is as large as possible, find $k+n$.
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant

user
839
Given that $\displaystyle {{\left((3!)!\right)!}\over{3!}}= k\cdot
n!$, where $k$ and $n$ are positive integers and $n$ is as large as possible, find $k+n$.
train