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Divisibility Rules Worksheet

Vedic maths trick 13: Divisibility tests · Set 736 · 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 70035 divisible by 29?
  2. 2.Is 22366 divisible by 6?
  3. 3.Is 22256 divisible by 4?
  4. 4.Is 106582 divisible by 23?
  5. 5.Is 60422 divisible by 19?
  6. 6.Is 109464 divisible by 24?
  7. 7.Is 49880 divisible by 8?
  8. 8.Is 75435 divisible by 15?
  9. 9.Is 8840 divisible by 5?
  10. 10.Is 123034 divisible by 23?
  11. 11.Is 70209 divisible by 24?
  12. 12.Is 13537 divisible by 3?
  13. 13.Is 68310 divisible by 23?
  14. 14.Is 65174 divisible by 15?
  15. 15.Is 70128 divisible by 18?
  16. 16.Is 38632 divisible by 8?
  17. 17.Is 3977 divisible by 12?
  18. 18.Is 3105 divisible by 9?
  19. 19.Is 27409 divisible by 11?
  20. 20.Is 78319 divisible by 17?
  21. 21.Is 6636 divisible by 24?
  22. 22.Is 5593 divisible by 3?
  23. 23.Is 10861 divisible by 4?
  24. 24.Is 31720 divisible by 10?
  25. 25.Is 44316 divisible by 12?
  26. 26.Is 37464 divisible by 24?
  27. 27.Is 15046 divisible by 8?
  28. 28.Is 39528 divisible by 18?
  29. 29.Is 19715 divisible by 7?
  30. 30.Is 22448 divisible by 7?
  31. 31.Is 26661 divisible by 5?
  32. 32.Is 54983 divisible by 9?
  33. 33.Is 10000 divisible by 4?
  34. 34.Is 1773 divisible by 9?
  35. 35.Is 31280 divisible by 20?
  36. 36.Is 8428 divisible by 6?
  37. 37.Is 25912 divisible by 11?
  38. 38.Is 41737 divisible by 13?
  39. 39.Is 15574 divisible by 13?
  40. 40.Is 77638 divisible by 13?

Answer key

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

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