Divisibility rules can sometimes be used to quickly determine whether one integer divides exactly into another.

There are divisibility rules which allow one to recognize certain divisors of a number from the number's digits.

The rule of nines, in mathematics, is a divisibility rule for the divisor 9.

See also Divisibility rule.

Stupid Divisibility Tricks Divisibility rules for 2-100.

A divisibility rule is a shorthand way of determining whether a given number is divisible by a fixed divisor without performing the division, usually by examining its digits.

Using a variation of the divisibility rule shortcut, the remainder from division by 9 can easily be found by adding the constituent digits and, if the sum still does not make the remainder obvious, adding the digits of the sum.

What this procedure does, as explained above for most divisibility rules, is simply subtract little by little multiples of 7 from the original number until reaching a number that is small enough for us to remember whether it is a multiple of 7.

In arithmetic, for example, when multiplying by 9, using the divisibility rule for 9 to verify that the sum of digits of the result is divisible by 9 is a sanity test - it will not catch every multiplication error, however it's a quick and simple method to discover many possible errors.