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Divisibility Rules Worksheet

Vedic maths trick 13: Divisibility tests · Set 220 · 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 18375 divisible by 3?
  2. 2.Is 57569 divisible by 9?
  3. 3.Is 10729 divisible by 3?
  4. 4.Is 43653 divisible by 13?
  5. 5.Is 66430 divisible by 10?
  6. 6.Is 98082 divisible by 18?
  7. 7.Is 13815 divisible by 15?
  8. 8.Is 42955 divisible by 15?
  9. 9.Is 13746 divisible by 12?
  10. 10.Is 7258 divisible by 11?
  11. 11.Is 20092 divisible by 3?
  12. 12.Is 56610 divisible by 30?
  13. 13.Is 17990 divisible by 5?
  14. 14.Is 86060 divisible by 13?
  15. 15.Is 103608 divisible by 24?
  16. 16.Is 46284 divisible by 12?
  17. 17.Is 18292 divisible by 3?
  18. 18.Is 62352 divisible by 12?
  19. 19.Is 24715 divisible by 7?
  20. 20.Is 26009 divisible by 11?
  21. 21.Is 27654 divisible by 4?
  22. 22.Is 48145 divisible by 19?
  23. 23.Is 14745 divisible by 9?
  24. 24.Is 28640 divisible by 29?
  25. 25.Is 34655 divisible by 23?
  26. 26.Is 338 divisible by 15?
  27. 27.Is 28624 divisible by 5?
  28. 28.Is 52861 divisible by 8?
  29. 29.Is 118740 divisible by 20?
  30. 30.Is 49006 divisible by 9?
  31. 31.Is 35830 divisible by 10?
  32. 32.Is 62417 divisible by 15?
  33. 33.Is 1683 divisible by 2?
  34. 34.Is 29263 divisible by 13?
  35. 35.Is 34704 divisible by 24?
  36. 36.Is 47560 divisible by 8?
  37. 37.Is 8880 divisible by 12?
  38. 38.Is 5220 divisible by 9?
  39. 39.Is 57885 divisible by 15?
  40. 40.Is 23248 divisible by 30?

Answer key

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

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