If 146 Is divisible by 5ⁿ, and then find the maximum value of n.

$$\eqalign{ & {\text{Required}}\,{\text{answer}}, \cr & = {\frac{{146}}{5}} + {\frac{{146}}{{{5^2}}}} + {\frac{{146}}{{{5^3}}}} \cr & = 29 + 5 + 1 \cr & = 35 \cr} $$
Note:
We have taken integral value only, not the fractional.
For example $$\frac{{146}}{5}$$ = 29.2 but we have taken 29 and so on.