Divisibility Rules - 1 .. 25

Here’s a comprehensive cheatsheet for the rules of divisibility, covering the top 25 rules to help you quickly determine whether a number is divisible by another:

Rules of Divisibility Cheatsheet

1. Divisibility by 1:

   • Any number is divisible by 1.

2. Divisibility by 2:

   • A number is divisible by 2 if its last digit is 0, 2, 4, 6, or 8.

3. Divisibility by 3:

   • A number is divisible by 3 if the sum of its digits is divisible by 3.

4. Divisibility by 4:

   • A number is divisible by 4 if the number formed by its last two digits is divisible by 4.

5. Divisibility by 5:

   • A number is divisible by 5 if its last digit is 0 or 5.

6. Divisibility by 6:

   • A number is divisible by 6 if it is divisible by both 2 and 3.

7. Divisibility by 7:

   • To check divisibility by 7, double the last digit and subtract it from the rest of the number. If the result is divisible by 7 (or 0), the original number is divisible by 7.

8. Divisibility by 8:

   • A number is divisible by 8 if the number formed by its last three digits is divisible by 8.

9. Divisibility by 9:

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

10. Divisibility by 10:

    • A number is divisible by 10 if its last digit is 0.

11. Divisibility by 11:

    • A number is divisible by 11 if the difference between the sum of the digits in odd positions and the sum of the digits in even positions is divisible by 11 (or 0).

12. Divisibility by 12:

    • A number is divisible by 12 if it is divisible by both 3 and 4.

13. Divisibility by 13:

    • To check divisibility by 13, remove the last digit, multiply it by 9, and subtract it from the rest of the number. If the result is divisible by 13 (or 0), the original number is divisible by 13.

14. Divisibility by 14:

    • A number is divisible by 14 if it is divisible by both 2 and 7.

15. Divisibility by 15:

    • A number is divisible by 15 if it is divisible by both 3 and 5.

16. Divisibility by 16:

    • A number is divisible by 16 if the number formed by its last four digits is divisible by 16.

17. Divisibility by 17:

    • To check divisibility by 17, remove the last digit, multiply it by 5, and subtract it from the rest of the number. If the result is divisible by 17 (or 0), the original number is divisible by 17.

18. Divisibility by 18:

    • A number is divisible by 18 if it is divisible by both 2 and 9.

19. Divisibility by 19:

    • To check divisibility by 19, remove the last digit, multiply it by 2, and subtract it from the rest of the number. If the result is divisible by 19 (or 0), the original number is divisible by 19.

20. Divisibility by 20:

    • A number is divisible by 20 if its last digit is 0 and the number formed by the last two digits is divisible by 4.

21. Divisibility by 21:

    • A number is divisible by 21 if it is divisible by both 3 and 7.

22. Divisibility by 22:

    • A number is divisible by 22 if it is divisible by both 2 and 11.

23. Divisibility by 23:

    • To check divisibility by 23, remove the last digit, multiply it by 7, and subtract it from the rest of the number. If the result is divisible by 23 (or 0), the original number is divisible by 23.

24. Divisibility by 24:

    • A number is divisible by 24 if it is divisible by both 3 and 8.

25. Divisibility by 25:

    • A number is divisible by 25 if its last two digits are 00, 25, 50, or 75.

Summary

These rules provide quick methods to determine if a number is divisible by another without performing full division. They are particularly useful for simplifying problems, solving equations, and verifying calculations.