Sometimes you don't need to calculate a whole division equation. Sometimes you just need to see if the equation will leave behind a remainder. To do this quickly, you can use these divisibility rules for certain numbers.

• When dividing by 2, if the last digit is even, or divisible by 2, then the whole number is divisible by 2. For example, with 698/2, the last digit is 8, which is even, therefore 698/2 will leave behind a whole number.
• When dividing by 3, if the sum of the digits is divisible by 3, then the whole number is divisible by 3. For example, with 5427/3, the sum of the digits of 5427 are 5 + 4 + 2 + 7, which is 18. If you want to go furthur you can check the sum of the digits of 18, which are 1 + 8 which equals 9, which is divisible by 3, therefore 5427 is divisible by 3
• When dividing by 4, if the last 2 digits are divisible by 2, then the whole number is divisible by 4. For example with 7564/4, the last 2 digits are 64, which is divisible by 4, therefore 7564/4 will leave behind a whole number.
• When dividing by 5, if the last digit is a 0 or a 5, then the whole number is divisible by 5, for example, with 6935/5, the last number is 5, therefore 6935 is divisible by 5.
• When dividing by 6, apply the divisibility rules for 2 and 3. If the number is divisible by both, then it is divisible by 6. For example with 3438/6, the last digit is 8, which is even, therefore it is divisible by 2. The sum of the digits is 3 + 4 + 3 + 8 which is 18, which is divisible by 3. Therefore it is divisble by 6
• When dividing by 8, if the last 3 digits are divisible by 8, then the whole number is divisible by 8. For example with 98728/8, 728 is divisible by 8, therefore 98728 is divisible by 8
• When dividing by 9, if the sum of the digits is equal to 9, then the whole number is equal to 9. For example with 7641/9, the sum of the digits of 7641 is 7 + 6 + 4 + 1 which equals 18, which is divisible by 9
• When dividing by 10, if the last digit is a 0, then the number is divisible by 10.