Rather than the conventional ways of prime factorization, there is an easy way to do the prime factorization of n!. First of all you have to list out all the prime numbers less than or equal to n. It is because
n! = 1 x 2 x 3 x 4 x 5 x .... x n
So prime factors of n! are all the prime numbers less than n. Next we have to find out the multiplicity of each of these prime factors.