$97$ is the largest prime less than $100$. What is the largest prime factor of $97!$ (97 factorial)?  (Reminder: The number $n!$ is the product of the integers from 1 to $n$.  For example, $5!=5\cdot 4\cdot3\cdot2\cdot 1= 120$.)
<|im_start|>system
You are a helpful assistant.<|im_end|>
<|im_start|>user
$97$ is the largest prime less than $100$. What is the largest prime factor of $97!$ (97 factorial)?  (Reminder: The number $n!$ is the product of the integers from 1 to $n$.  For example, $5!=5\cdot 4\cdot3\cdot2\cdot 1= 120$.)
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant

user
97
$97$ is the largest prime less than $100$. What is the largest prime factor of $97!$ (97 factorial)?  (Reminder: The number $n!$ is the product of the integers from 1 to $n$.  For example, $5!=5\cdot 4\cdot3\cdot2\cdot 1= 120$.)
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