Find the highest power of 1980 such that

Question

I am asked to find the highest power of $1980$ that divides the integer $$N=\frac{(1980n)!}{(n!)^{1980}}$$ I have no idea where to start, since the factorials don't seem able to be simplified. Can you please give me a hint or a boost that could help?

Answer 1

Legendre's formula for the exponent of a prime in a factorial may be useful, as well as the factorization $1980 = 2^2 \cdot 3^2 \cdot 5 \cdot 11$.

But I don't think there's a very simple formula for the answer. For $n$ from $1$ to $20$ I get $$197, 394, 493, 790, 493, 988, 1384, 986, 493, 988, 197, 394, 592, 790, 989, 986, 1385, 988, 1482, 1976$$