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If 300!=3^(m)xxan integer, then find the...

If 300!=`3^(m)xx`an integer, then find the value of m .

A

m=148

B

m=150

C

It is equivalent to number of n is 150!`=2^(n-2)xx`an integer

D

`m=.^(150)C_(2)`

Text Solution

Verified by Experts

The correct Answer is:
A
`E_(3)(300!)=[300/3]+[300/3^(2)]+[300/3^(3)]+[300/3^(4)]+[300/3^(5)]`
`=100+33+11+3+1=148`
`thereforem=148`
and `E_(2)(150!)=[150/2]+[150/2^(2)]+[150/2^(3)]+ . . .+[150/2^(7)]`
`=75+37+18+9+4+2+1=146`
`thereforen-2=146`
`impliesn=148`
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