How to determine whether a number is divisible by 7 (idea)

   12345
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  | 1 2 3 3
7 |86415

Your method is great, and it works. But why go about it in such a roundabout way?

Downvote all you like, it's a neat trick, it works. I don't dispute that. I still hold that simple long division is faster.

Sure, you can cut the roof off your car with an angle grinder, climb in, hotwire the ignition and drive from point A to point B in reverse and you'll still get there. Why bother unless you're simply trying to show off, though? Using the key is far far simpler and still gets you the same result.