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Divisibility Rules Worksheet

Vedic maths trick 13: Divisibility tests · Set 674 · 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 103466 divisible by 20?
  2. 2.Is 28657 divisible by 6?
  3. 3.Is 4557 divisible by 7?
  4. 4.Is 28393 divisible by 11?
  5. 5.Is 60490 divisible by 10?
  6. 6.Is 5017 divisible by 29?
  7. 7.Is 16760 divisible by 5?
  8. 8.Is 102630 divisible by 15?
  9. 9.Is 13705 divisible by 17?
  10. 10.Is 46380 divisible by 20?
  11. 11.Is 100572 divisible by 29?
  12. 12.Is 14688 divisible by 17?
  13. 13.Is 113543 divisible by 17?
  14. 14.Is 21100 divisible by 17?
  15. 15.Is 724 divisible by 3?
  16. 16.Is 9693 divisible by 2?
  17. 17.Is 32688 divisible by 24?
  18. 18.Is 104880 divisible by 19?
  19. 19.Is 12989 divisible by 2?
  20. 20.Is 18410 divisible by 5?
  21. 21.Is 18473 divisible by 13?
  22. 22.Is 17030 divisible by 5?
  23. 23.Is 2120 divisible by 5?
  24. 24.Is 53838 divisible by 18?
  25. 25.Is 16141 divisible by 7?
  26. 26.Is 15258 divisible by 5?
  27. 27.Is 15216 divisible by 19?
  28. 28.Is 95910 divisible by 15?
  29. 29.Is 110561 divisible by 19?
  30. 30.Is 21615 divisible by 12?
  31. 31.Is 2297 divisible by 7?
  32. 32.Is 3005 divisible by 5?
  33. 33.Is 80142 divisible by 19?
  34. 34.Is 12432 divisible by 7?
  35. 35.Is 8137 divisible by 2?
  36. 36.Is 124963 divisible by 19?
  37. 37.Is 20820 divisible by 6?
  38. 38.Is 7889 divisible by 23?
  39. 39.Is 18376 divisible by 4?
  40. 40.Is 8750 divisible by 2?

Answer key

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

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