3. For a positive integer $n$, if $n=p q\left(p \geqslant q, p, q \in \mathbf{N}_{+}\right)$, when $p-q$ is the smallest, then $p q$ is called the "best factorization" of $n$, and it is defined that $f(n)=\frac{q}{p}$ (for example, the factorizations of 12 are $12 \times 1$, $6 \times 2$, $4 \times 3$, among which, $4 \times 3$ is the best factorization of 12, then $f(12)=\frac{3}{4}$). Regarding $f(n)$, there are the following four judgments:
(1) $f(4)=0$;
(2) $f(7)=\frac{1}{7}$;
(3) $f(24)=\frac{3}{8}$;
(4) $f(2012)=\frac{4}{503}$.
Among them, the correct judgments are
3. (2) 、(4).

Notice,
$$
\begin{array}{l}
4=2 \times 2,7=7 \times 1,24=6 \times 4, \\
2012=503 \times 4 .
\end{array}
$$

Then $f(4)=1, f(7)=\frac{1}{7}$,
$$
f(24)=\frac{2}{3}, f(2012)=\frac{4}{503} \text {. }
$$

Therefore, (1) and (3) are incorrect, (2) and (4) are correct.