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
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.