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Divisibility Rules Worksheet

Vedic maths trick 13: Divisibility tests · Set 36 · 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 54260 divisible by 20?
  2. 2.Is 104764 divisible by 18?
  3. 3.Is 6289 divisible by 15?
  4. 4.Is 53372 divisible by 11?
  5. 5.Is 111763 divisible by 23?
  6. 6.Is 152112 divisible by 24?
  7. 7.Is 117151 divisible by 29?
  8. 8.Is 59625 divisible by 9?
  9. 9.Is 133380 divisible by 20?
  10. 10.Is 53584 divisible by 17?
  11. 11.Is 8985 divisible by 2?
  12. 12.Is 45484 divisible by 13?
  13. 13.Is 39063 divisible by 29?
  14. 14.Is 21024 divisible by 9?
  15. 15.Is 27438 divisible by 7?
  16. 16.Is 37418 divisible by 12?
  17. 17.Is 21376 divisible by 4?
  18. 18.Is 23748 divisible by 12?
  19. 19.Is 13927 divisible by 2?
  20. 20.Is 150930 divisible by 30?
  21. 21.Is 40516 divisible by 6?
  22. 22.Is 3037 divisible by 3?
  23. 23.Is 105544 divisible by 20?
  24. 24.Is 18588 divisible by 12?
  25. 25.Is 47164 divisible by 13?
  26. 26.Is 78910 divisible by 13?
  27. 27.Is 44858 divisible by 19?
  28. 28.Is 6519 divisible by 5?
  29. 29.Is 12321 divisible by 17?
  30. 30.Is 3080 divisible by 8?
  31. 31.Is 16590 divisible by 30?
  32. 32.Is 22972 divisible by 13?
  33. 33.Is 128763 divisible by 19?
  34. 34.Is 77620 divisible by 20?
  35. 35.Is 71420 divisible by 12?
  36. 36.Is 21696 divisible by 4?
  37. 37.Is 20288 divisible by 3?
  38. 38.Is 923 divisible by 3?
  39. 39.Is 127144 divisible by 23?
  40. 40.Is 61866 divisible by 9?

Answer key

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

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