7. If 653 divides $\overline{a b 2347}$, then $a+b=$

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【Answer】 11
【Solution】Since $653|\overline{a b 2347} \Leftrightarrow 653|(\overline{a b 2347}+653)$, considering $\overline{a b 2347}+653=\overline{a b 3000}$, so $653 \mid \overline{a b 3} \times 1000$. Since 653 is a prime number, and 653 cannot divide 1000, it follows that $653 \mid \overline{a b 3}$, thus leading to $\left\{\begin{array}{l}a=6 \\ b=5\end{array}\right.$, so $a+b=11$