Is it Divisible?
The 6-digit number is divisible by 7, 8, and 9. What values can A, B, and C take?
Enter your answer as the sum of the sums for all triples that work.
The answer is 34.
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1 solution
l c m ( 7 , 8 , 9 ) = 7 . 8 . 9 = 5 0 4 .
We must choose a number of the form 739ABC such that it is a multiple of 7, 8 and 9;
i.e. we must choose a number of the form 739ABC that is divisible by lcm(7, 8, 9) = 504.
Now 739 000 gives remainder 136 on division by 504. Hence the numbers 739ABC we are looking for, are of form
7 3 9 0 0 0 − 1 3 6 + k . 5 0 4
where k is an integer. We can see that k can only be 1 or 2. If k = 1 , we get the number
739 368 so that one solution for A, B, C is
A = 3 , B = 6 , C = 8
and if k = 2 we get the number 739 872 so that another solution for A, B, C is
A = 8 , B = 7 , C = 2 .