Question

The exponent of 3 in 100! is?

Answer 1

`48`

Explanation:

The exponent of `3` in `100!` is

`=[100/3]+[100/3^2]+[100/3^3]+[100/3^4]+[100/3^5]+\ldots`

`=[33.\bar{3}]+[11.\bar1]+[3.\bar{703}]+[1.234...]+[0.411...]+\ldots`

`=33+11+3+1+0+\ldots`

`=48`