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Divisibility Rules Worksheet

Vedic maths trick 13: Divisibility tests · Set 200 · 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 21813 divisible by 9?
  2. 2.Is 113760 divisible by 20?
  3. 3.Is 95236 divisible by 29?
  4. 4.Is 2388 divisible by 8?
  5. 5.Is 8164 divisible by 2?
  6. 6.Is 129490 divisible by 23?
  7. 7.Is 27772 divisible by 8?
  8. 8.Is 42475 divisible by 8?
  9. 9.Is 17691 divisible by 3?
  10. 10.Is 9891 divisible by 8?
  11. 11.Is 132690 divisible by 30?
  12. 12.Is 8802 divisible by 7?
  13. 13.Is 7215 divisible by 3?
  14. 14.Is 5826 divisible by 2?
  15. 15.Is 26373 divisible by 5?
  16. 16.Is 65113 divisible by 19?
  17. 17.Is 54140 divisible by 20?
  18. 18.Is 33787 divisible by 23?
  19. 19.Is 71858 divisible by 12?
  20. 20.Is 14364 divisible by 12?
  21. 21.Is 102658 divisible by 20?
  22. 22.Is 8706 divisible by 18?
  23. 23.Is 152014 divisible by 23?
  24. 24.Is 12825 divisible by 5?
  25. 25.Is 3055 divisible by 5?
  26. 26.Is 10899 divisible by 7?
  27. 27.Is 9556 divisible by 4?
  28. 28.Is 50613 divisible by 29?
  29. 29.Is 12702 divisible by 7?
  30. 30.Is 11880 divisible by 4?
  31. 31.Is 14928 divisible by 3?
  32. 32.Is 11801 divisible by 6?
  33. 33.Is 11377 divisible by 2?
  34. 34.Is 12198 divisible by 19?
  35. 35.Is 108344 divisible by 29?
  36. 36.Is 63013 divisible by 11?
  37. 37.Is 58742 divisible by 23?
  38. 38.Is 15240 divisible by 8?
  39. 39.Is 636 divisible by 2?
  40. 40.Is 29541 divisible by 23?

Answer key

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

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