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You may have used shortcuts to see if a number is divisible by another. example "is...

You may have used shortcuts to see if a number is divisible by another. example "is a number is divisible by 4 if the last two digits form a number divisible by 4" or "a number is divisible by 8 if the last three digits form a number divisible by 8." Where do they come from? Why are some numbers left out? Could you prove these shortcuts?

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