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Divisibility Rules Worksheet

Vedic maths trick 13: Divisibility tests · Set 322 · 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 41059 divisible by 15?
  2. 2.Is 22629 divisible by 23?
  3. 3.Is 149089 divisible by 29?
  4. 4.Is 59700 divisible by 12?
  5. 5.Is 33288 divisible by 19?
  6. 6.Is 14610 divisible by 5?
  7. 7.Is 9850 divisible by 20?
  8. 8.Is 38648 divisible by 8?
  9. 9.Is 24577 divisible by 7?
  10. 10.Is 69636 divisible by 12?
  11. 11.Is 2681 divisible by 7?
  12. 12.Is 33093 divisible by 12?
  13. 13.Is 27258 divisible by 7?
  14. 14.Is 8536 divisible by 5?
  15. 15.Is 21924 divisible by 7?
  16. 16.Is 1415 divisible by 5?
  17. 17.Is 34068 divisible by 5?
  18. 18.Is 26614 divisible by 29?
  19. 19.Is 31320 divisible by 6?
  20. 20.Is 155311 divisible by 30?
  21. 21.Is 7758 divisible by 8?
  22. 22.Is 5829 divisible by 15?
  23. 23.Is 60086 divisible by 17?
  24. 24.Is 194160 divisible by 30?
  25. 25.Is 173070 divisible by 30?
  26. 26.Is 13684 divisible by 4?
  27. 27.Is 19377 divisible by 3?
  28. 28.Is 64647 divisible by 11?
  29. 29.Is 8265 divisible by 5?
  30. 30.Is 2832 divisible by 3?
  31. 31.Is 5186 divisible by 12?
  32. 32.Is 5123 divisible by 12?
  33. 33.Is 44434 divisible by 13?
  34. 34.Is 11347 divisible by 19?
  35. 35.Is 38945 divisible by 8?
  36. 36.Is 41177 divisible by 19?
  37. 37.Is 1795 divisible by 5?
  38. 38.Is 139624 divisible by 23?
  39. 39.Is 26848 divisible by 8?
  40. 40.Is 94720 divisible by 20?

Answer key

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

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