4. Add three digits after 764 to make the resulting six-digit number divisible by 8, 9, and 11.
(Let the six-digit number be $\overline{764 a b c}$. Let $M=7+4$ $+b=11+b, N=c+a+6$. Then $\overline{a b c}$ is divisible by 8, $M+N=17+a+b+c$ is divisible by 9, $M-N=$ $5+b-a-c$ is divisible by 11. It is easy to see that $17 \leqslant M+N \leqslant$ $44,-13 \leqslant M-N \leqslant 14$. Therefore, $M+N=18,27,36$, $M-N=-11,0,11$. Exhaustive search yields the unique solution 764 280.)