14. (15 points) Given that the two-digit natural number “HuWei” can be divided by the product of its digits, find the two-digit number represented by “HuWei”.


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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)
$$
\begin{array}{l}
\text { (1) } Y=1 \\
(K-10) X=1 \\
X=1, \quad K=11
\end{array}
$$

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

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

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

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

So Hu Wei $=15$;
(6) $Y=6$
$(3K-5) X=3$
$$
X=3, K=2
$$

So Hu Wei $=36$
(7) $Y=7$, using the same method, no solution;
(8) $Y=8$, using the same method, no solution;
(9) $Y=9$, using the same method, no solution;

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