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divisibility by 37 (Posted on 2024-11-20)

Determine the number of five digit integers 37ABC, such that 37ABC, 37BCA, 37CAB is divisible by 37.

No Solution Yet Submitted by Danish Ahmed Khan

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The choice of 37ABC instead of ABC was so that a digit can be zero.

Of the 27 multiples of 37 under 1000, ALL of them work!

037, 370, 703

074, 740, 407

111,111,111 etc...

I wrote them all down before noticing.

I never knew this fact (I haven't proved it yet) but the answer is 27.

Posted by Jer on 2024-11-20 10:37:47

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