Exponent of 12in100!

1
by buntyyrttrt
bunty.. you should select best answer only after proper explanation is given. do not select before.

2014-11-26T21:09:56+05:30

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Exponent of a prime number p  in a number N  is given as  a  if
N = p^a * M,  where  M is the product of all remaining factors.

If p, q, r are prime numbers or relatively prime, then
N = p^a * q^b * r^c * ...

Then exponent of (pq) in N is the smaller of the two numbers a and b.

Exponent of a number p in N!  is given by the expression :

This is so because,  there are N/p multiples of p in N like p, 2p, 3p etc., then for each p^2, there is one extra p.  For p^3 , there is one more extra  p  as compared to p^2.   Hence we get the above formula.

12 = 2^2 * 3.  So we find exponents of 2 and 3 in 100 !.    Then we find exponent of 12.

Hence exponent of 12 in 100! is 48.