10. How many numbers of the form $\overline{a b c d a b c d}$ can be divisible by 18769.
【Analysis】$\overline{a b c d a b c d}=\overline{a b c d} \times 10001=\overline{a b c d} \times 73 \times 137,18769=137^{2}$, so to make $\overline{a b c d a b c d}$ divisible by 18769, it is only necessary to make $\overline{a b c d}$ divisible by 137, $137 \times 7=959,137 \times 8=1096$, $137 \times 72=9864,137 \times 73=10001$, so there are $72-8+1=65$ numbers that meet the requirement.