Elusive scenario

Number Theory Level 3

If the six digit integer 739 A B C ‾ \overline{739ABC} is divisible by 7, 8, and 9. What is the sum of all possible values A A , B B and C C ?


The answer is 34.

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Abdeslem Smahi by Abdeslem Smahi , 24, Algeria

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1 solution

7 × 8 × 9 = 504. 7 \times 8 \times 9 = 504.

739000/504= 1466.2...

504 × 1467 = 739638 504 \times 1467=739638 and 504 × 1468 = 739872 504 \times 1468=739872 .

6 + 3 + 8 + 8 + 7 + 2 = 34 6+3+8+8+7+2=34

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