prime-factorization

The number of divisors of $$2100$$ is ___________.

The number of distinct positive integral factors of 2014 is _______ .

The exponent of $$11$$ in the prime factorization of $$300!$$ is

Let $$n = {p^2}q,$$ where $$p$$ and $$q$$ are distinct prime numbers. How many numbers $$m$$ satisfy $$1 \le m \le n$$ and $$gcd\left( {m.n} \right) = 1?$$ Note that $$gcd(m,n)$$ i...