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Divisibility Rules - 26 .. 55

1. Divisibility by 26

  • Rule: A number is divisible by 26 if it is divisible by both 2 and 13.

2. Divisibility by 27

  • Rule: A number is divisible by 27 if the sum of the digits of the number, each multiplied by 3 (or the alternating sum of these multiples), is divisible by 27.

3. Divisibility by 28

  • Rule: A number is divisible by 28 if it is divisible by both 4 and 7.

4. Divisibility by 29

  • Rule: To check divisibility by 29, remove the last digit, multiply it by 3, and subtract it from the rest of the number. If the result is divisible by 29 (or 0), the original number is divisible by 29.

5. Divisibility by 30

  • Rule: A number is divisible by 30 if it is divisible by 2, 3, and 5.

6. Divisibility by 31

  • Rule: To check divisibility by 31, remove the last digit, multiply it by 3, and add it to the rest of the number. If the result is divisible by 31 (or 0), the original number is divisible by 31.

7. Divisibility by 32

  • Rule: A number is divisible by 32 if the number formed by its last five digits is divisible by 32.

8. Divisibility by 33

  • Rule: A number is divisible by 33 if it is divisible by both 3 and 11.

9. Divisibility by 34

  • Rule: A number is divisible by 34 if it is divisible by both 2 and 17.

10. Divisibility by 35

  • Rule: A number is divisible by 35 if it is divisible by both 5 and 7.

11. Divisibility by 36

  • Rule: A number is divisible by 36 if it is divisible by both 4 and 9.

12. Divisibility by 37

  • Rule: To check divisibility by 37, remove the last digit, multiply it by 3, and add it to the rest of the number. If the result is divisible by 37 (or 0), the original number is divisible by 37.

13. Divisibility by 38

  • Rule: A number is divisible by 38 if it is divisible by both 2 and 19.

14. Divisibility by 39

  • Rule: A number is divisible by 39 if it is divisible by both 3 and 13.

15. Divisibility by 40

  • Rule: A number is divisible by 40 if its last two digits form a number divisible by 40.

16. Divisibility by 41

  • Rule: To check divisibility by 41, remove the last digit, multiply it by 5, and add it to the rest of the number. If the result is divisible by 41 (or 0), the original number is divisible by 41.

17. Divisibility by 42

  • Rule: A number is divisible by 42 if it is divisible by both 6 and 7.

18. Divisibility by 43

  • Rule: To check divisibility by 43, remove the last digit, multiply it by 9, and subtract it from the rest of the number. If the result is divisible by 43 (or 0), the original number is divisible by 43.

19. Divisibility by 44

  • Rule: A number is divisible by 44 if it is divisible by both 4 and 11.

20. Divisibility by 45

  • Rule: A number is divisible by 45 if it is divisible by both 5 and 9.

21. Divisibility by 46

  • Rule: A number is divisible by 46 if it is divisible by both 2 and 23.

22. Divisibility by 47

  • Rule: To check divisibility by 47, remove the last digit, multiply it by 2, and subtract it from the rest of the number. If the result is divisible by 47 (or 0), the original number is divisible by 47.

23. Divisibility by 48

  • Rule: A number is divisible by 48 if it is divisible by both 3 and 16.

24. Divisibility by 49

  • Rule: A number is divisible by 49 if the number formed by its last two digits is divisible by 49, or if the alternating sum of blocks of 2 digits starting from the end is divisible by 49.

25. Divisibility by 50

  • Rule: A number is divisible by 50 if its last digit is 0 and the second last digit is either 0 or 5.

Additional Clever Rules

  1. Divisibility by 51:

    • A number is divisible by 51 if it is divisible by both 3 and 17.

  2. Divisibility by 52:

    • A number is divisible by 52 if it is divisible by both 4 and 13.

  3. Divisibility by 53:

    • To check divisibility by 53, remove the last digit, multiply it by 9, and add it to the rest of the number. If the result is divisible by 53 (or 0), the original number is divisible by 53.

  4. Divisibility by 54:

    • A number is divisible by 54 if it is divisible by both 6 and 9.

  5. Divisibility by 55:

    • A number is divisible by 55 if it is divisible by both 5 and 11.

These additional rules can help in quickly determining the divisibility of numbers and simplifying mathematical problems.