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We are talking about positive, negative integers and 0. For negative integers, we take its magnitude.

1. Every integer number is divisible by 1

2. The units digit should be even.

3. Sum of all digits must be divisible by 3.

4. The number formed by the last two digits should be divisible by 4.

5. the units digit should be 5 or 0.

6. The number should be divisible by 2 and 3. Apply those two rules.

7. Subtract twice the units digit from the remaining number. The remainder should be divisible by 7. Continue the same procedure.

8. The number formed by the last 3 digits should be divisible by 8.

9. The sum of the digits must be divisible by 9.

10. The units digit must be 0.

11. The sum of digits in even places = sum of digits in odd places in the number.

Or, the difference between two sums is divisible by 11.

13. Add 4 times the units digit to the number remaining. That should be divisible by 13. Repeat the steps, if the number is big.

17. Subtract 5 times the units digit from the number formed by the rest. That should be divisible by 17. Repeat the procedure if the number is big.

19. Add twice the last digit to the number formed by the rest. That should be divisible by 19. Repeat the procedure if the number is big.

1. Every integer number is divisible by 1

2. The units digit should be even.

3. Sum of all digits must be divisible by 3.

4. The number formed by the last two digits should be divisible by 4.

5. the units digit should be 5 or 0.

6. The number should be divisible by 2 and 3. Apply those two rules.

7. Subtract twice the units digit from the remaining number. The remainder should be divisible by 7. Continue the same procedure.

8. The number formed by the last 3 digits should be divisible by 8.

9. The sum of the digits must be divisible by 9.

10. The units digit must be 0.

11. The sum of digits in even places = sum of digits in odd places in the number.

Or, the difference between two sums is divisible by 11.

13. Add 4 times the units digit to the number remaining. That should be divisible by 13. Repeat the steps, if the number is big.

17. Subtract 5 times the units digit from the number formed by the rest. That should be divisible by 17. Repeat the procedure if the number is big.

19. Add twice the last digit to the number formed by the rest. That should be divisible by 19. Repeat the procedure if the number is big.