2. $48 n$ is the smallest positive integer that satisfies the following conditions:
(1) $n$ is a multiple of 75;
(2) $n$ has exactly 75 positive divisors (including 1 and itself). Find $\frac{n}{75}$.
[Solution] Since $75=5 \times 5 \times 3, n$ has exactly 75 divisors, and $n$ is a multiple of 75, so
$$
n=75 k=3 \times 5^{2} k \geqslant 2^{4} \times 3^{4} \times 5^{2} .
$$

By the minimality of $n$, we have $\frac{n}{75}=k=2^{4} \times 3^{3}=432$.