Divisibility rules

A number is divisible by 9 if and only if the sum of its digits is divisible by 9.

1. Add all the known digits of the number.
2. Find what is needed to reach the next multiple of 9.
3. Insert one digit so that the complete digit sum becomes a multiple of 9.

Check the result by adding all digits again. If the sum is 9, 18, 27 and so on, the divisibility rule for 9 is satisfied.

A number is divisible by a divisor when division leaves no remainder. For 2, the last digit must be even; for 5, it must be 0 or 5; for 10, it must be 0. For 3 or 9, the sum of the digits must be divisible by 3 or 9 respectively. Both divisibility rules must hold for the same number.

A number is divisible by a divisor when division leaves no remainder. For 2, the last digit must be even; for 5, it must be 0 or 5; for 10, it must be 0. For 3 or 9, the sum of the digits must be divisible by 3 or 9 respectively. Choose the number that fails the specified divisibility rule.

Find the division remainder. If it is 0, nothing needs to be added. Otherwise subtract the remainder from the divisor to find the amount needed to reach the next multiple. For example, 17 divided by 5 leaves 2, so add 5 − 2 = 3.

A number is divisible by a divisor when division leaves no remainder. For 2, the last digit must be even; for 5, it must be 0 or 5; for 10, it must be 0. For 3 or 9, the sum of the digits must be divisible by 3 or 9 respectively. Check each option using the rule for the specified divisor.

Find the division remainder. If it is 0, nothing needs to be added. Otherwise subtract the remainder from the divisor to find the amount needed to reach the next multiple. For example, 17 divided by 5 leaves 2, so add 5 − 2 = 3.

Find the first multiple of the divisor strictly greater than the given number. Divide the number by the divisor, take the whole-number quotient, add 1 and multiply by the divisor. If the original number is already divisible, you still need the next multiple.