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Divisibility Rules Worksheet

Vedic maths trick 13: Divisibility tests · Set 95 · 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 31176 divisible by 6?
  2. 2.Is 47385 divisible by 15?
  3. 3.Is 118082 divisible by 17?
  4. 4.Is 26871 divisible by 13?
  5. 5.Is 51415 divisible by 13?
  6. 6.Is 17178 divisible by 10?
  7. 7.Is 20476 divisible by 23?
  8. 8.Is 1874 divisible by 2?
  9. 9.Is 36413 divisible by 8?
  10. 10.Is 162458 divisible by 29?
  11. 11.Is 12315 divisible by 15?
  12. 12.Is 37440 divisible by 9?
  13. 13.Is 120878 divisible by 19?
  14. 14.Is 12719 divisible by 7?
  15. 15.Is 13471 divisible by 19?
  16. 16.Is 4360 divisible by 8?
  17. 17.Is 35611 divisible by 8?
  18. 18.Is 60885 divisible by 13?
  19. 19.Is 7321 divisible by 9?
  20. 20.Is 22255 divisible by 5?
  21. 21.Is 11014 divisible by 5?
  22. 22.Is 74670 divisible by 15?
  23. 23.Is 10357 divisible by 3?
  24. 24.Is 14148 divisible by 6?
  25. 25.Is 22282 divisible by 4?
  26. 26.Is 19089 divisible by 6?
  27. 27.Is 51225 divisible by 15?
  28. 28.Is 1229 divisible by 2?
  29. 29.Is 4360 divisible by 3?
  30. 30.Is 110186 divisible by 20?
  31. 31.Is 3079 divisible by 10?
  32. 32.Is 25225 divisible by 7?
  33. 33.Is 11814 divisible by 30?
  34. 34.Is 45630 divisible by 18?
  35. 35.Is 67309 divisible by 15?
  36. 36.Is 3219 divisible by 11?
  37. 37.Is 15033 divisible by 4?
  38. 38.Is 54562 divisible by 10?
  39. 39.Is 9930 divisible by 12?
  40. 40.Is 10472 divisible by 3?

Answer key

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

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