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Divisibility Rules Worksheet

Vedic maths trick 13: Divisibility tests · Set 457 · 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 2456 divisible by 9?
  2. 2.Is 62657 divisible by 23?
  3. 3.Is 5320 divisible by 17?
  4. 4.Is 98430 divisible by 17?
  5. 5.Is 26220 divisible by 20?
  6. 6.Is 24334 divisible by 18?
  7. 7.Is 12700 divisible by 10?
  8. 8.Is 65399 divisible by 19?
  9. 9.Is 54144 divisible by 12?
  10. 10.Is 36235 divisible by 6?
  11. 11.Is 22806 divisible by 6?
  12. 12.Is 7379 divisible by 2?
  13. 13.Is 63545 divisible by 18?
  14. 14.Is 10718 divisible by 3?
  15. 15.Is 132375 divisible by 23?
  16. 16.Is 46097 divisible by 7?
  17. 17.Is 81430 divisible by 17?
  18. 18.Is 83153 divisible by 13?
  19. 19.Is 3781 divisible by 2?
  20. 20.Is 116301 divisible by 19?
  21. 21.Is 44514 divisible by 8?
  22. 22.Is 66788 divisible by 23?
  23. 23.Is 11941 divisible by 8?
  24. 24.Is 70956 divisible by 29?
  25. 25.Is 5465 divisible by 3?
  26. 26.Is 44759 divisible by 23?
  27. 27.Is 3286 divisible by 4?
  28. 28.Is 12992 divisible by 2?
  29. 29.Is 3123 divisible by 9?
  30. 30.Is 6456 divisible by 3?
  31. 31.Is 29172 divisible by 11?
  32. 32.Is 97020 divisible by 18?
  33. 33.Is 163950 divisible by 30?
  34. 34.Is 36017 divisible by 8?
  35. 35.Is 10914 divisible by 3?
  36. 36.Is 89520 divisible by 24?
  37. 37.Is 18945 divisible by 10?
  38. 38.Is 8151 divisible by 19?
  39. 39.Is 27341 divisible by 19?
  40. 40.Is 46928 divisible by 15?

Answer key

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

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