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Divisibility Rules Worksheet

Vedic maths trick 13: Divisibility tests · Set 395 · 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 24883 divisible by 6?
  2. 2.Is 122815 divisible by 29?
  3. 3.Is 14247 divisible by 9?
  4. 4.Is 169904 divisible by 29?
  5. 5.Is 173727 divisible by 29?
  6. 6.Is 106800 divisible by 24?
  7. 7.Is 12232 divisible by 5?
  8. 8.Is 13967 divisible by 8?
  9. 9.Is 20670 divisible by 5?
  10. 10.Is 2601 divisible by 17?
  11. 11.Is 368 divisible by 4?
  12. 12.Is 8606 divisible by 3?
  13. 13.Is 10853 divisible by 7?
  14. 14.Is 96301 divisible by 30?
  15. 15.Is 24392 divisible by 30?
  16. 16.Is 43368 divisible by 13?
  17. 17.Is 34060 divisible by 6?
  18. 18.Is 41993 divisible by 7?
  19. 19.Is 29025 divisible by 5?
  20. 20.Is 32980 divisible by 5?
  21. 21.Is 111057 divisible by 30?
  22. 22.Is 52707 divisible by 29?
  23. 23.Is 61258 divisible by 10?
  24. 24.Is 3919 divisible by 3?
  25. 25.Is 31392 divisible by 8?
  26. 26.Is 160402 divisible by 23?
  27. 27.Is 5969 divisible by 4?
  28. 28.Is 10167 divisible by 4?
  29. 29.Is 78925 divisible by 17?
  30. 30.Is 79962 divisible by 30?
  31. 31.Is 14352 divisible by 5?
  32. 32.Is 131204 divisible by 20?
  33. 33.Is 86598 divisible by 17?
  34. 34.Is 20880 divisible by 20?
  35. 35.Is 75972 divisible by 13?
  36. 36.Is 12789 divisible by 29?
  37. 37.Is 93279 divisible by 17?
  38. 38.Is 14500 divisible by 5?
  39. 39.Is 5112 divisible by 9?
  40. 40.Is 49629 divisible by 15?

Answer key

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

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