14. Given that the two-digit natural number "Hu Wei" can be divided by the product of its digits, find the two-digit number represented by "Hu Wei".


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【Analysis】From the problem, we know that the two-digit number "Hu Wei" must satisfy: the two-digit natural number "Hu Wei" can be divided by the product of its digits. With these two conditions, we can sequentially test to draw a conclusion.

【Solution】Let Hu be $X$ and Wei be $Y$, then: the problem states: $10X + Y = X \times Y \times K$ (where $K$ is an integer)
(1) $Y=1$
$$
\begin{array}{l}
(K-10) X=1 \\
X=1, \quad K=11
\end{array}
$$

So Hu Wei $=11$;
(2) $Y=2$
$$
\begin{array}{l}
(K-5) X=1 \\
X=1, \quad K=6
\end{array}
$$

So Hu Wei $=12$;
(3) $Y=3$
$$
(3K-10) X=3
$$

No solution;
(4) $Y=4$
$$
\begin{array}{l}
(4XK-10K)=2 \\
X=2, \quad K=3
\end{array}
$$

So Hu Wei $=24$;
(5) $Y=5$
$$
\begin{array}{l}
(K-2) X=1 \\
X=1, \quad K=3
\end{array}
$$

So Hu Wei $=15$;
(6) $Y=6$
$$
\begin{array}{l}
(3K-5) X=3 \\
X=3, \quad K=2
\end{array}
$$

So Hu Wei $=36$
(7) $Y=7$, similarly, no solution;
(8) $Y=8$, similarly, no solution;
(9) $Y=9$, similarly, no solution;

In summary, there are five two-digit numbers that satisfy the problem, i.e., $11, 12, 15, 24, 36$.