Searching for $n$

Consider the number $3\times 47^3 = 311469$ . The number of factor 47 present in it is $311469/47 + 311469/47^2+311469/47^3=6771$ . Note that this is the minimum value of $n$ that results in it being divisible by $47^{6771}$ . However, observe that $311468! = 311469!/311469$ which results in elimination of 3 powers of 47 from its prime factorization. 311468! and factorials of positive integers smaller than 311468 are now at most divisible by $47^{6768}$ . Hence the conditions stated in the question cannot be satisfied by any natural number so the answer is 0.