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Find the exponent of 3 in 100!....

Find the exponent of 3 in 100!.

Text Solution

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In terms of prime factors 100! Can be written as `2^(a)*3^(b)*5^(c)*7^(d)`
Now, `b=E_(3)(100!)`
`=[(100)/(3)]+[(100)/(3^(4))]+[(100)/(3^(3))]+[(100)/(3^(4))]` + . . .
`=33+11+3+1+0+ . . .=48`
Hence, exponent of 3 is 48.
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