# Divisibility Rules Rules may refer to the last digit of a number as $y$ and the number formed by all other digits as $x$. That is for a number $n$, $n = 10x + y$. | F | Rule | | ---:| --------------------------------------------------------- | | 2 | Last digit must be divisible by 2 | | 3 | The sum of its digits is divisible by 3 | | 4 | The number formed by the last 2 digits is divisible by 4 | | 5 | The last digit is either 0 or 5 | | 6 | The number is divisible by 2 and 3 | | 7 | $x-2y$ is divisible by 7 | | 8 | The number formed by the last 3 digits is divisible by 8 | | 9 | The sum of all digits is divisible by 9 | | 10 | The last digit is 0 | | 11 | The alternating sum of digits is divisible by 11 | | 12 | The number is divisible by 3 and 4 | | 13 | $x+4y$ is divisible by 13 | | 14 | The number is divisible by 7 and 2 | | 15 | The number is divisible by 5 and 3 | | 16 | The number formed by the last 4 digits is divisible by 16 | | 17 | $x-5y$ is divisible by 17 | | 18 | The number is divisible by 9 and 2 | | 19 | $x+2y$ is divisible by 19 | | 20 | The number formed by the last 2 digits is divisible by 20 | | 21 | $x-2y$ is divisible by 19 | | 23 | $x+7y$ is divisible by 23 | | 29 | $x+3y$ is divisible by 29 | ## Resources - *[Divisibility Rules](https://en.wikipedia.org/wiki/Divisibility_rule)*. Wikipedia.