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Divisibility Rules Worksheet

Vedic maths trick 13: Divisibility tests · Set 569 · 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 125619 divisible by 29?
  2. 2.Is 23972 divisible by 13?
  3. 3.Is 62608 divisible by 12?
  4. 4.Is 21208 divisible by 11?
  5. 5.Is 4047 divisible by 3?
  6. 6.Is 7602 divisible by 3?
  7. 7.Is 181590 divisible by 30?
  8. 8.Is 43070 divisible by 11?
  9. 9.Is 7002 divisible by 18?
  10. 10.Is 22771 divisible by 8?
  11. 11.Is 13293 divisible by 9?
  12. 12.Is 83544 divisible by 24?
  13. 13.Is 8428 divisible by 4?
  14. 14.Is 9338 divisible by 29?
  15. 15.Is 46046 divisible by 7?
  16. 16.Is 15432 divisible by 5?
  17. 17.Is 103841 divisible by 20?
  18. 18.Is 63192 divisible by 29?
  19. 19.Is 5743 divisible by 3?
  20. 20.Is 24780 divisible by 7?
  21. 21.Is 65418 divisible by 15?
  22. 22.Is 8436 divisible by 3?
  23. 23.Is 42129 divisible by 9?
  24. 24.Is 17188 divisible by 3?
  25. 25.Is 70958 divisible by 17?
  26. 26.Is 12636 divisible by 4?
  27. 27.Is 39909 divisible by 8?
  28. 28.Is 146759 divisible by 23?
  29. 29.Is 6571 divisible by 9?
  30. 30.Is 7817 divisible by 5?
  31. 31.Is 9941 divisible by 2?
  32. 32.Is 8171 divisible by 2?
  33. 33.Is 131376 divisible by 24?
  34. 34.Is 2753 divisible by 2?
  35. 35.Is 3416 divisible by 7?
  36. 36.Is 38502 divisible by 9?
  37. 37.Is 34581 divisible by 7?
  38. 38.Is 134376 divisible by 24?
  39. 39.Is 780 divisible by 20?
  40. 40.Is 34815 divisible by 29?

Answer key

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

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