Solution
The maximum value of n will be equal to the number of powers of 5 in the expansion of 146!.
This will be equal to whole number values of: $$\frac{146}{5}+\frac{29}{5}+\frac{5}{5}=29\ +\ 5\ +\ 1\ =\ 35$$.
So, the maximum value that n can take is 35.
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