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the exponent of 15 in 100!, is...

the exponent of `15` in `100!,` is

A

48

B

24

C

25

D

23

Text Solution

Verified by Experts

The correct Answer is:
B
We have, `15=3xx5`
Now,
`E_(3)(100!)=48`
[See illustration 1]
and `E_(5)(100!)=[(100)/(5)]+[(100)/(5^(2))]=20+4=24`
`:.` Exponent of 15 in 100!=min (24,48) =24.
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Statement-1: The number of zeros at the end of 100! Is, 24. Statement-2: The exponent of prine p in n!, is [(n)/(p)]+[(n)/(p^(2))]+.......+[(n)/(p^(r))] Where r is a natural number such that P^(r)lenltP^(r+1) .

OBJECTIVE RD SHARMA ENGLISH-PERMUTATIONS AND COMBINATIONS-Chapter Test
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