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Divisibility Rules Worksheet

Vedic maths trick 13: Divisibility tests · Set 763 · 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 11167 divisible by 9?
  2. 2.Is 11634 divisible by 3?
  3. 3.Is 64409 divisible by 13?
  4. 4.Is 64461 divisible by 15?
  5. 5.Is 59606 divisible by 30?
  6. 6.Is 12101 divisible by 7?
  7. 7.Is 5300 divisible by 20?
  8. 8.Is 95491 divisible by 19?
  9. 9.Is 12132 divisible by 4?
  10. 10.Is 39476 divisible by 10?
  11. 11.Is 23147 divisible by 20?
  12. 12.Is 50320 divisible by 20?
  13. 13.Is 78843 divisible by 23?
  14. 14.Is 123218 divisible by 19?
  15. 15.Is 93960 divisible by 15?
  16. 16.Is 58608 divisible by 12?
  17. 17.Is 82667 divisible by 30?
  18. 18.Is 37460 divisible by 20?
  19. 19.Is 34295 divisible by 9?
  20. 20.Is 55880 divisible by 11?
  21. 21.Is 33524 divisible by 12?
  22. 22.Is 58272 divisible by 12?
  23. 23.Is 42380 divisible by 10?
  24. 24.Is 10514 divisible by 2?
  25. 25.Is 33444 divisible by 12?
  26. 26.Is 15413 divisible by 10?
  27. 27.Is 52344 divisible by 9?
  28. 28.Is 8750 divisible by 5?
  29. 29.Is 18536 divisible by 4?
  30. 30.Is 77390 divisible by 13?
  31. 31.Is 3348 divisible by 4?
  32. 32.Is 115181 divisible by 23?
  33. 33.Is 9112 divisible by 17?
  34. 34.Is 28344 divisible by 6?
  35. 35.Is 59800 divisible by 20?
  36. 36.Is 39862 divisible by 11?
  37. 37.Is 34989 divisible by 7?
  38. 38.Is 83449 divisible by 13?
  39. 39.Is 63234 divisible by 18?
  40. 40.Is 38310 divisible by 30?

Answer key

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

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