Find the exponent of 80 in 200!.

Explanation

`because80=2^(4)xx5`
`thereforeE_(2)(180!)=[180/2]+[180/2^(2)]+[180/2^(3)]+[180/2^(4)]+[180/2^(5)]+[180/2^(6)]+[180/2^(7)]+` . . .
`=90+45+22+11+5+2+1=176`
and `E_(5)(180!)=[180/5]+[180/5^(2)]+[180/5^(3)]+ . . .`
`=36+7+1+0+ . . .`
`=44`
Now, exponennt of 16 in `180!` is `[176/4]=44`. where `[*]` denotes the greatest integer function. hence, the exponent of 80 in 180! is 44.