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Divisibility Rules Worksheet

Vedic maths trick 13: Divisibility tests · Set 211 · 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 186042 divisible by 29?
  2. 2.Is 57360 divisible by 12?
  3. 3.Is 57330 divisible by 18?
  4. 4.Is 99016 divisible by 19?
  5. 5.Is 7825 divisible by 24?
  6. 6.Is 25937 divisible by 18?
  7. 7.Is 38626 divisible by 7?
  8. 8.Is 133320 divisible by 24?
  9. 9.Is 9221 divisible by 3?
  10. 10.Is 84780 divisible by 15?
  11. 11.Is 53107 divisible by 13?
  12. 12.Is 6978 divisible by 6?
  13. 13.Is 464 divisible by 2?
  14. 14.Is 12072 divisible by 2?
  15. 15.Is 17130 divisible by 3?
  16. 16.Is 103426 divisible by 18?
  17. 17.Is 48870 divisible by 18?
  18. 18.Is 52807 divisible by 13?
  19. 19.Is 147798 divisible by 23?
  20. 20.Is 1284 divisible by 12?
  21. 21.Is 2430 divisible by 18?
  22. 22.Is 8848 divisible by 10?
  23. 23.Is 15529 divisible by 4?
  24. 24.Is 14651 divisible by 23?
  25. 25.Is 60885 divisible by 9?
  26. 26.Is 152738 divisible by 29?
  27. 27.Is 46425 divisible by 20?
  28. 28.Is 27863 divisible by 6?
  29. 29.Is 175 divisible by 2?
  30. 30.Is 60124 divisible by 24?
  31. 31.Is 3670 divisible by 6?
  32. 32.Is 13804 divisible by 17?
  33. 33.Is 57487 divisible by 30?
  34. 34.Is 4491 divisible by 3?
  35. 35.Is 16540 divisible by 23?
  36. 36.Is 63297 divisible by 13?
  37. 37.Is 17757 divisible by 9?
  38. 38.Is 43369 divisible by 24?
  39. 39.Is 4514 divisible by 2?
  40. 40.Is 14098 divisible by 6?

Answer key

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

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