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Divisibility Rules Worksheet

Vedic maths trick 13: Divisibility tests · Set 711 · 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 29467 divisible by 7?
  2. 2.Is 26801 divisible by 8?
  3. 3.Is 104640 divisible by 15?
  4. 4.Is 30286 divisible by 19?
  5. 5.Is 382 divisible by 13?
  6. 6.Is 26017 divisible by 4?
  7. 7.Is 77012 divisible by 13?
  8. 8.Is 59432 divisible by 9?
  9. 9.Is 43280 divisible by 13?
  10. 10.Is 70333 divisible by 30?
  11. 11.Is 91756 divisible by 19?
  12. 12.Is 13735 divisible by 5?
  13. 13.Is 12227 divisible by 4?
  14. 14.Is 32340 divisible by 7?
  15. 15.Is 2861 divisible by 2?
  16. 16.Is 46800 divisible by 9?
  17. 17.Is 23797 divisible by 30?
  18. 18.Is 9728 divisible by 3?
  19. 19.Is 130604 divisible by 24?
  20. 20.Is 32382 divisible by 9?
  21. 21.Is 27225 divisible by 7?
  22. 22.Is 44343 divisible by 17?
  23. 23.Is 7165 divisible by 3?
  24. 24.Is 30587 divisible by 9?
  25. 25.Is 30229 divisible by 15?
  26. 26.Is 28250 divisible by 5?
  27. 27.Is 21824 divisible by 11?
  28. 28.Is 64860 divisible by 20?
  29. 29.Is 105229 divisible by 29?
  30. 30.Is 7276 divisible by 17?
  31. 31.Is 74551 divisible by 20?
  32. 32.Is 8142 divisible by 7?
  33. 33.Is 9817 divisible by 8?
  34. 34.Is 19836 divisible by 29?
  35. 35.Is 39340 divisible by 20?
  36. 36.Is 14580 divisible by 7?
  37. 37.Is 52380 divisible by 15?
  38. 38.Is 27374 divisible by 4?
  39. 39.Is 42799 divisible by 23?
  40. 40.Is 68313 divisible by 17?

Answer key

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

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