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Divisibility Rules Worksheet

Vedic maths trick 13: Divisibility tests · Set 932 · 40 sums
TalentJR

The trick (Ekadhikena Purvena): 2, 5, 10: the last digit (even; 0 or 5; 0). 3 and 9: add the digits. 4: the last two digits. 8: the last three digits. 6: even and passes the rule for 3. 11: from the right, add the 1st, 3rd, 5th… digits and the 2nd, 4th… digits; the difference must be 0 or a multiple of 11. Any prime p: multiply p by 1, 3, 7 or 9 so it ends in 9; one more than the digits before the 9 is the osculator (7 → 5, 13 → 4, 17 → 12, 19 → 2, 23 → 7, 29 → 3). Take the last digit × the osculator and add it to the rest; repeat until the number is small and check the times table. Composite numbers: split into two factors that share no factor and pass BOTH rules — 6 = 2 × 3, 12 = 3 × 4, 15 = 3 × 5, 18 = 2 × 9, 20 = 4 × 5, 24 = 3 × 8, 30 = 3 × 10.

NameDateTime takenScore ___ / 40
  1. 1.Is 90974 divisible by 13?
  2. 2.Is 56520 divisible by 24?
  3. 3.Is 60335 divisible by 19?
  4. 4.Is 29297 divisible by 11?
  5. 5.Is 2387 divisible by 5?
  6. 6.Is 18037 divisible by 17?
  7. 7.Is 128872 divisible by 29?
  8. 8.Is 117222 divisible by 23?
  9. 9.Is 27855 divisible by 5?
  10. 10.Is 6050 divisible by 5?
  11. 11.Is 10988 divisible by 7?
  12. 12.Is 27892 divisible by 9?
  13. 13.Is 30978 divisible by 6?
  14. 14.Is 37856 divisible by 13?
  15. 15.Is 52200 divisible by 8?
  16. 16.Is 77513 divisible by 13?
  17. 17.Is 47340 divisible by 20?
  18. 18.Is 31826 divisible by 19?
  19. 19.Is 59844 divisible by 12?
  20. 20.Is 11461 divisible by 3?
  21. 21.Is 18306 divisible by 9?
  22. 22.Is 53941 divisible by 29?
  23. 23.Is 14107 divisible by 5?
  24. 24.Is 139649 divisible by 24?
  25. 25.Is 36613 divisible by 29?
  26. 26.Is 24771 divisible by 23?
  27. 27.Is 105179 divisible by 17?
  28. 28.Is 123491 divisible by 19?
  29. 29.Is 56796 divisible by 23?
  30. 30.Is 14382 divisible by 20?
  31. 31.Is 1504 divisible by 8?
  32. 32.Is 237 divisible by 3?
  33. 33.Is 2568 divisible by 2?
  34. 34.Is 26519 divisible by 13?
  35. 35.Is 46821 divisible by 20?
  36. 36.Is 17420 divisible by 4?
  37. 37.Is 175022 divisible by 29?
  38. 38.Is 114323 divisible by 23?
  39. 39.Is 53270 divisible by 12?
  40. 40.Is 40939 divisible by 29?

Answer key

  1. yes
  2. yes
  3. no
  4. no
  5. no
  6. yes
  7. no
  8. no
  9. yes
  10. yes
  11. no
  12. no
  13. yes
  14. yes
  15. yes
  16. no
  17. yes
  18. no
  19. yes
  20. no
  21. yes
  22. no
  23. no
  24. no
  25. no
  26. yes
  27. yes
  28. no
  29. no
  30. no
  31. yes
  32. yes
  33. yes
  34. no
  35. no
  36. yes
  37. no
  38. no
  39. no
  40. no

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