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Divisibility Rules Worksheet

Vedic maths trick 13: Divisibility tests · Set 72 · 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 5422 divisible by 3?
  2. 2.Is 39975 divisible by 15?
  3. 3.Is 56721 divisible by 15?
  4. 4.Is 5955 divisible by 7?
  5. 5.Is 40449 divisible by 10?
  6. 6.Is 16279 divisible by 3?
  7. 7.Is 32501 divisible by 9?
  8. 8.Is 5135 divisible by 2?
  9. 9.Is 48134 divisible by 7?
  10. 10.Is 174665 divisible by 29?
  11. 11.Is 5844 divisible by 5?
  12. 12.Is 13162 divisible by 5?
  13. 13.Is 30237 divisible by 10?
  14. 14.Is 119139 divisible by 19?
  15. 15.Is 60859 divisible by 24?
  16. 16.Is 56126 divisible by 11?
  17. 17.Is 96493 divisible by 18?
  18. 18.Is 58245 divisible by 11?
  19. 19.Is 56050 divisible by 10?
  20. 20.Is 115614 divisible by 18?
  21. 21.Is 169980 divisible by 30?
  22. 22.Is 15891 divisible by 4?
  23. 23.Is 52400 divisible by 30?
  24. 24.Is 55183 divisible by 13?
  25. 25.Is 9724 divisible by 2?
  26. 26.Is 89100 divisible by 20?
  27. 27.Is 30844 divisible by 30?
  28. 28.Is 57840 divisible by 20?
  29. 29.Is 42201 divisible by 8?
  30. 30.Is 23761 divisible by 5?
  31. 31.Is 97467 divisible by 24?
  32. 32.Is 57945 divisible by 30?
  33. 33.Is 54442 divisible by 20?
  34. 34.Is 62707 divisible by 19?
  35. 35.Is 17680 divisible by 20?
  36. 36.Is 139140 divisible by 20?
  37. 37.Is 30632 divisible by 5?
  38. 38.Is 42487 divisible by 7?
  39. 39.Is 15416 divisible by 7?
  40. 40.Is 111566 divisible by 19?

Answer key

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

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