7. Modify one digit of 31743, you can get a multiple of 823, what is the modified number?

 

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7. 33743
7.【Solution】 $31743 \div 823=38 \cdots \cdots \cdot 469$
No matter which of the last three digits 7, 4, 3 is changed, it cannot make the remainder increase or decrease to become a multiple of 823. If the thousand's digit 1 is changed to 3, then since $2469=823 \times 3$, we get that 33743 is divisible by 823. If the ten-thousand's digit is changed, the result differs from 33743 by a two-digit number $\times 1000$, and thus is not divisible by 823, so the modified number is 33743.