Call me stupid, but
wouldn't long division
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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.