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Divisibility Rules Worksheet

Vedic maths trick 13: Divisibility tests · Set 886 · 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 50070 divisible by 30?
  2. 2.Is 103260 divisible by 20?
  3. 3.Is 28917 divisible by 10?
  4. 4.Is 62840 divisible by 13?
  5. 5.Is 9468 divisible by 7?
  6. 6.Is 17017 divisible by 15?
  7. 7.Is 166310 divisible by 24?
  8. 8.Is 34188 divisible by 12?
  9. 9.Is 9495 divisible by 2?
  10. 10.Is 47060 divisible by 10?
  11. 11.Is 9419 divisible by 6?
  12. 12.Is 141744 divisible by 24?
  13. 13.Is 636 divisible by 6?
  14. 14.Is 55120 divisible by 8?
  15. 15.Is 29934 divisible by 7?
  16. 16.Is 7174 divisible by 6?
  17. 17.Is 11481 divisible by 11?
  18. 18.Is 5394 divisible by 20?
  19. 19.Is 94980 divisible by 20?
  20. 20.Is 117717 divisible by 19?
  21. 21.Is 11107 divisible by 4?
  22. 22.Is 21454 divisible by 4?
  23. 23.Is 8604 divisible by 3?
  24. 24.Is 3034 divisible by 2?
  25. 25.Is 24362 divisible by 13?
  26. 26.Is 8799 divisible by 7?
  27. 27.Is 11312 divisible by 4?
  28. 28.Is 4875 divisible by 2?
  29. 29.Is 26552 divisible by 4?
  30. 30.Is 7840 divisible by 8?
  31. 31.Is 145176 divisible by 24?
  32. 32.Is 39498 divisible by 29?
  33. 33.Is 77976 divisible by 19?
  34. 34.Is 88020 divisible by 15?
  35. 35.Is 15669 divisible by 5?
  36. 36.Is 6114 divisible by 3?
  37. 37.Is 10483 divisible by 2?
  38. 38.Is 102853 divisible by 18?
  39. 39.Is 68860 divisible by 13?
  40. 40.Is 105510 divisible by 30?

Answer key

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

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