Divisible by 9? You can tell without dividing.
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There is a quick test for almost every small divisor, and most people only know the ones for 2, 5 and 10. The useful ones are these: a number divides by 3 if its digits add to a multiple of 3, by 9 if they add to a multiple of 9, by 4 if the last two digits do, by 6 if it passes both the 2 and 3 tests, and by 11 if the alternating sum of its digits divides by 11.
Each round tells you which rule applied, so the reasoning is visible rather than just the verdict.
This version: The last-two-digits family. Your best score is saved in this browser, so you can come back and try to beat it. Nothing is uploaded and no sign-up is needed.
Because 10 leaves remainder 1 when divided by 9, so every power of ten does too. That means a number and its digit sum always leave the same remainder — a small, elegant result.
There is one — double the last digit and subtract it from the rest — but it is barely faster than dividing, which is why it is rarely taught. This game leaves it out on purpose.
Simplifying fractions, spotting factors quickly, and checking arithmetic. If you can see instantly that 4,725 divides by 9, cancelling fractions gets much faster.