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## How Many Digits?

Our base-$10$ system makes it easy to check whether a number is divisible by certain numbers. For example, checking whether $356$ is divisible by $2$ or $5$ comes down to checking whether the last digit is a multiple of either number. In this case, our number is divisible by $2,$ but not by $5.$

Why does this work, though? Are there similar shortcuts for $4$ and other numbers? Keep reading to find out, or skip ahead to the challenge for a puzzle on this idea.