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Divisibility Rules Worksheet

Vedic maths trick 13: Divisibility tests · Set 474 · 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 22885 divisible by 6?
  2. 2.Is 11682 divisible by 12?
  3. 3.Is 12891 divisible by 3?
  4. 4.Is 7008 divisible by 12?
  5. 5.Is 22156 divisible by 29?
  6. 6.Is 3314 divisible by 5?
  7. 7.Is 2364 divisible by 11?
  8. 8.Is 5569 divisible by 2?
  9. 9.Is 20058 divisible by 5?
  10. 10.Is 6218 divisible by 8?
  11. 11.Is 9828 divisible by 6?
  12. 12.Is 61267 divisible by 15?
  13. 13.Is 153323 divisible by 29?
  14. 14.Is 28382 divisible by 11?
  15. 15.Is 35672 divisible by 13?
  16. 16.Is 115420 divisible by 20?
  17. 17.Is 5686 divisible by 11?
  18. 18.Is 40775 divisible by 10?
  19. 19.Is 49824 divisible by 12?
  20. 20.Is 13392 divisible by 18?
  21. 21.Is 18506 divisible by 19?
  22. 22.Is 13541 divisible by 2?
  23. 23.Is 3996 divisible by 2?
  24. 24.Is 517 divisible by 2?
  25. 25.Is 57086 divisible by 17?
  26. 26.Is 18622 divisible by 12?
  27. 27.Is 18810 divisible by 10?
  28. 28.Is 49224 divisible by 12?
  29. 29.Is 31959 divisible by 12?
  30. 30.Is 17486 divisible by 7?
  31. 31.Is 1284 divisible by 3?
  32. 32.Is 71841 divisible by 24?
  33. 33.Is 102309 divisible by 24?
  34. 34.Is 78778 divisible by 17?
  35. 35.Is 98662 divisible by 18?
  36. 36.Is 36184 divisible by 7?
  37. 37.Is 5899 divisible by 5?
  38. 38.Is 108281 divisible by 19?
  39. 39.Is 8784 divisible by 9?
  40. 40.Is 208830 divisible by 30?

Answer key

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

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