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Divisibility Rules Worksheet

Vedic maths trick 13: Divisibility tests · Set 31 · 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 60127 divisible by 9?
  2. 2.Is 15600 divisible by 10?
  3. 3.Is 50370 divisible by 23?
  4. 4.Is 66290 divisible by 10?
  5. 5.Is 23401 divisible by 6?
  6. 6.Is 28440 divisible by 18?
  7. 7.Is 120843 divisible by 29?
  8. 8.Is 90774 divisible by 18?
  9. 9.Is 25695 divisible by 5?
  10. 10.Is 164053 divisible by 29?
  11. 11.Is 75460 divisible by 20?
  12. 12.Is 15463 divisible by 7?
  13. 13.Is 142164 divisible by 29?
  14. 14.Is 34790 divisible by 12?
  15. 15.Is 18355 divisible by 12?
  16. 16.Is 7362 divisible by 3?
  17. 17.Is 41295 divisible by 19?
  18. 18.Is 469 divisible by 20?
  19. 19.Is 66264 divisible by 12?
  20. 20.Is 46897 divisible by 17?
  21. 21.Is 74796 divisible by 12?
  22. 22.Is 4870 divisible by 11?
  23. 23.Is 13576 divisible by 6?
  24. 24.Is 4980 divisible by 10?
  25. 25.Is 9761 divisible by 18?
  26. 26.Is 6896 divisible by 4?
  27. 27.Is 33230 divisible by 5?
  28. 28.Is 30338 divisible by 18?
  29. 29.Is 2816 divisible by 6?
  30. 30.Is 16070 divisible by 6?
  31. 31.Is 14400 divisible by 9?
  32. 32.Is 11269 divisible by 2?
  33. 33.Is 35712 divisible by 24?
  34. 34.Is 25100 divisible by 29?
  35. 35.Is 5695 divisible by 17?
  36. 36.Is 41752 divisible by 8?
  37. 37.Is 31887 divisible by 9?
  38. 38.Is 13706 divisible by 7?
  39. 39.Is 29533 divisible by 17?
  40. 40.Is 8315 divisible by 7?

Answer key

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

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