Example 1-6 $n=7^{3} \times 11^{2} \times 13^{4}$, find the number of integers that divide $n$ evenly.

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Obviously, the integers that can divide $n$ are
$$
7 l_{1} \times 11^{l_{2}} \times 13^{l_{3}}, \quad 0 \leqslant l_{1} \leqslant 3,0 \leqslant l_{2} \leqslant 2,0 \leqslant l_{3} \leqslant 4 \text {. }
$$

According to the multiplication rule, the number of integers that can divide $n$ is
$$
4 \times 3 \times 5=60
$$