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Find the largest number n such that (2012!)! is divisible by ((n!)!)!.........where n! is the product of 1st n positive integers.
WE HAVE,
x! is divisible by r! if x>r.
this implies that
(2012!)! is divisible by ((n!)!)! if 2012!>(n!)!
2012>n!
the greatest value of n which satisfies it is 6.
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