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Divisibility Rules Worksheet

Vedic maths trick 13: Divisibility tests · Set 853 · 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 7718 divisible by 2?
  2. 2.Is 13990 divisible by 11?
  3. 3.Is 64260 divisible by 10?
  4. 4.Is 31591 divisible by 10?
  5. 5.Is 9555 divisible by 7?
  6. 6.Is 56580 divisible by 12?
  7. 7.Is 11912 divisible by 3?
  8. 8.Is 37468 divisible by 8?
  9. 9.Is 189983 divisible by 29?
  10. 10.Is 12684 divisible by 7?
  11. 11.Is 26031 divisible by 24?
  12. 12.Is 44009 divisible by 7?
  13. 13.Is 105990 divisible by 30?
  14. 14.Is 98430 divisible by 17?
  15. 15.Is 38301 divisible by 17?
  16. 16.Is 9089 divisible by 4?
  17. 17.Is 127806 divisible by 19?
  18. 18.Is 757 divisible by 2?
  19. 19.Is 14550 divisible by 3?
  20. 20.Is 6885 divisible by 2?
  21. 21.Is 42366 divisible by 23?
  22. 22.Is 16887 divisible by 3?
  23. 23.Is 155844 divisible by 24?
  24. 24.Is 59375 divisible by 19?
  25. 25.Is 11785 divisible by 11?
  26. 26.Is 12810 divisible by 9?
  27. 27.Is 41100 divisible by 6?
  28. 28.Is 69311 divisible by 19?
  29. 29.Is 91437 divisible by 29?
  30. 30.Is 40127 divisible by 6?
  31. 31.Is 7893 divisible by 7?
  32. 32.Is 9822 divisible by 6?
  33. 33.Is 2247 divisible by 2?
  34. 34.Is 20845 divisible by 6?
  35. 35.Is 37177 divisible by 12?
  36. 36.Is 148108 divisible by 29?
  37. 37.Is 6123 divisible by 13?
  38. 38.Is 5516 divisible by 29?
  39. 39.Is 199646 divisible by 29?
  40. 40.Is 23840 divisible by 5?

Answer key

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

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