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Answer: 3816547290
Why?
First try 258:
The remaining possibilities are 1472589630 and 7412589630, but neither of 1472589 and 7412589 are divisible by 7
Next try 654:
The remaining possibilities are 1836547290, 1896543270, 1896547230, 7896543210, 3816547290, 9816543270 and 9816547230
Out of 1836547, 1896543, 1896547, 7896543, 3816547, 9816543 and 9816547, only 3816547 is a multiple of 7.