Answer is 48. Find the exponents of 2² and 3 pick the smaller one.

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Answer is 48. Find the exponents of 2² and 3 pick the smaller one.

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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

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.

N = p^a * M, where M is the product of all remaining factors.

If p, q, r are prime numbers or relatively prime, then

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.