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While it is possible to come up with divisibility rules for any number, some divisibility rules are more complicated than others, and in some cases it becomes easier to just carry out the division.

A rule that works for 8 is: If the last three digits of a number are divisible by 8, then the entire number is divisible by 8.

For 7: Separate a number's last three digits, and divide from the remaining number. If the result is divisible by 7, the original number is divisible by 7. For example, in 31969, separate as 31; 969. Subtracting the second part from the first will give you a negative number, but you can also subtract the other way: 969 - 31. Since the result is divisible by 7, the original number also is.

This SAME rule also works for 11 and 13, and is based on the fact that 7, 11 and 13 are factors of 1001.

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