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Divisibility Rules Worksheet

Vedic maths trick 13: Divisibility tests · Set 198 · 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 11758 divisible by 3?
  2. 2.Is 28722 divisible by 6?
  3. 3.Is 117743 divisible by 30?
  4. 4.Is 1457 divisible by 20?
  5. 5.Is 6815 divisible by 5?
  6. 6.Is 30786 divisible by 7?
  7. 7.Is 16831 divisible by 13?
  8. 8.Is 26600 divisible by 7?
  9. 9.Is 14745 divisible by 24?
  10. 10.Is 50324 divisible by 12?
  11. 11.Is 184035 divisible by 30?
  12. 12.Is 9706 divisible by 18?
  13. 13.Is 542 divisible by 2?
  14. 14.Is 4980 divisible by 20?
  15. 15.Is 9030 divisible by 13?
  16. 16.Is 29352 divisible by 8?
  17. 17.Is 3664 divisible by 6?
  18. 18.Is 8903 divisible by 20?
  19. 19.Is 13004 divisible by 2?
  20. 20.Is 166997 divisible by 29?
  21. 21.Is 11180 divisible by 13?
  22. 22.Is 103000 divisible by 20?
  23. 23.Is 87087 divisible by 29?
  24. 24.Is 2487 divisible by 2?
  25. 25.Is 24408 divisible by 24?
  26. 26.Is 8146 divisible by 3?
  27. 27.Is 10057 divisible by 6?
  28. 28.Is 36800 divisible by 20?
  29. 29.Is 101035 divisible by 17?
  30. 30.Is 16506 divisible by 7?
  31. 31.Is 55488 divisible by 18?
  32. 32.Is 7325 divisible by 2?
  33. 33.Is 29261 divisible by 29?
  34. 34.Is 11905 divisible by 5?
  35. 35.Is 7629 divisible by 23?
  36. 36.Is 30843 divisible by 20?
  37. 37.Is 63138 divisible by 17?
  38. 38.Is 2670 divisible by 5?
  39. 39.Is 102545 divisible by 18?
  40. 40.Is 74249 divisible by 19?

Answer key

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

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