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Divisibility Rules Worksheet

Vedic maths trick 13: Divisibility tests · Set 448 · 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 49012 divisible by 9?
  2. 2.Is 20790 divisible by 15?
  3. 3.Is 16066 divisible by 8?
  4. 4.Is 100572 divisible by 17?
  5. 5.Is 24096 divisible by 4?
  6. 6.Is 163189 divisible by 29?
  7. 7.Is 22962 divisible by 9?
  8. 8.Is 154824 divisible by 24?
  9. 9.Is 32831 divisible by 7?
  10. 10.Is 40503 divisible by 23?
  11. 11.Is 20187 divisible by 10?
  12. 12.Is 78266 divisible by 20?
  13. 13.Is 5805 divisible by 9?
  14. 14.Is 44316 divisible by 9?
  15. 15.Is 34025 divisible by 24?
  16. 16.Is 2983 divisible by 4?
  17. 17.Is 19350 divisible by 6?
  18. 18.Is 17640 divisible by 3?
  19. 19.Is 1673 divisible by 7?
  20. 20.Is 54763 divisible by 23?
  21. 21.Is 103045 divisible by 20?
  22. 22.Is 129300 divisible by 20?
  23. 23.Is 79995 divisible by 15?
  24. 24.Is 7113 divisible by 2?
  25. 25.Is 32376 divisible by 29?
  26. 26.Is 22269 divisible by 20?
  27. 27.Is 5716 divisible by 30?
  28. 28.Is 27657 divisible by 4?
  29. 29.Is 18975 divisible by 6?
  30. 30.Is 142317 divisible by 29?
  31. 31.Is 134008 divisible by 24?
  32. 32.Is 41623 divisible by 10?
  33. 33.Is 151524 divisible by 24?
  34. 34.Is 63037 divisible by 13?
  35. 35.Is 41524 divisible by 13?
  36. 36.Is 21450 divisible by 5?
  37. 37.Is 73371 divisible by 12?
  38. 38.Is 36100 divisible by 10?
  39. 39.Is 32123 divisible by 13?
  40. 40.Is 63549 divisible by 30?

Answer key

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

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