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There is one for 7, although it is not very useful. Take the last digit, truncate it and double it. Then subtract it from the rest. If the resulting number is divisible by 7, so was the original. For 8, if the last 3 digits are divisible by, so is the number in question. For example, 72248 is divisible by 8 because 248 is. And 259 is divisible by 7 because 9 times 2 is 18, and 25 minus 18 is 7... Voila!

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Q: What are the divisibility rules for 7 and 8?
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