114 The sides of a right triangle are all positive integers. One of the legs is 1575 less than the hypotenuse, and the other leg is less than 1991. Then the length of the hypotenuse of this right triangle is $\qquad$ .
1141799 . Let the hypotenuse of a right-angled triangle be $c$, and the two legs be $a$ and $b$. Then
$$
\begin{aligned}
a^{2} & =c^{2}-b^{2}=(c-b)(c+b) \\
& =1575 \times(c+b) \\
& =3^{2} \times 5^{2} \times 7 \times(c+b),
\end{aligned}
$$

Thus, $105 \mid a$. Also, $a^{2}=1575(c+b)>1575 a$, so
$$
1575<a<1991 .
$$

Therefore,
$$
105 \times 15<a<105 \times 19 .
$$

Since $c-b$ is odd, $c+b$ is also odd, hence $a$ is odd,
$$
a=105 \times 17=1785 .
$$

Furthermore, $c=1799$.