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Divisibility Rules Worksheet

Vedic maths trick 13: Divisibility tests · Set 138 · 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 32173 divisible by 20?
  2. 2.Is 2424 divisible by 10?
  3. 3.Is 89451 divisible by 13?
  4. 4.Is 49509 divisible by 9?
  5. 5.Is 4317 divisible by 6?
  6. 6.Is 82161 divisible by 17?
  7. 7.Is 29830 divisible by 18?
  8. 8.Is 5559 divisible by 6?
  9. 9.Is 50159 divisible by 20?
  10. 10.Is 107066 divisible by 17?
  11. 11.Is 4142 divisible by 5?
  12. 12.Is 110520 divisible by 30?
  13. 13.Is 112873 divisible by 23?
  14. 14.Is 702 divisible by 10?
  15. 15.Is 55440 divisible by 9?
  16. 16.Is 33418 divisible by 11?
  17. 17.Is 27621 divisible by 7?
  18. 18.Is 75825 divisible by 30?
  19. 19.Is 89448 divisible by 15?
  20. 20.Is 2177 divisible by 7?
  21. 21.Is 24831 divisible by 9?
  22. 22.Is 68723 divisible by 19?
  23. 23.Is 6930 divisible by 3?
  24. 24.Is 59690 divisible by 11?
  25. 25.Is 34160 divisible by 10?
  26. 26.Is 131699 divisible by 19?
  27. 27.Is 8817 divisible by 4?
  28. 28.Is 64516 divisible by 15?
  29. 29.Is 9793 divisible by 2?
  30. 30.Is 27048 divisible by 12?
  31. 31.Is 109531 divisible by 17?
  32. 32.Is 51696 divisible by 9?
  33. 33.Is 12171 divisible by 3?
  34. 34.Is 123002 divisible by 24?
  35. 35.Is 42990 divisible by 15?
  36. 36.Is 77393 divisible by 19?
  37. 37.Is 35609 divisible by 10?
  38. 38.Is 13588 divisible by 9?
  39. 39.Is 97951 divisible by 15?
  40. 40.Is 157392 divisible by 24?

Answer key

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

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