Divisibility rule

A divisibility rule is a rule you can use to determine a number's divisibility by another number. In decimal, the divisibility rules are:

Every number is divisible by 1
A number is divisible by 2 if it ends in 0, 2, 4, 6, or 8.
Add the digits. The resulting number is divisible by 3 iff the original number was.
Last 2 digits must be divisible by 4.
Must end in 0 or 5
Must be divisible by 2 and 3
Subtract twice the last digit from the original. The resulting number is divisible by 7 iff the original number was.
Last 3 digits must be divisible by 8. (If you don't know the divisibility of a 3-digit number by 8, subtract 200 to check to see.)
Add the digits. The resulting number is divisible by 9 iff the original number was.
Must end in 0
Add the digits in odd places and add the digits in even places. The difference between these numbers is divisible by 11 iff the original number was.
Check divisibility by 3 and 4
Add 4 times the last digit to the original number. The resulting number is divisible by 13 iff the original number was.
Check divisibility by 2 and 7
Check divisibility by 3 and 5
Last 4 digits must be divisible by 16. (If you don't know the divisibility of a 4-digit number by 16, subtract a multiple of 2000 or 400.)

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