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Divisibility Rules Worksheet

Vedic maths trick 13: Divisibility tests · Set 744 · 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 27927 divisible by 29?
  2. 2.Is 84271 divisible by 17?
  3. 3.Is 18029 divisible by 11?
  4. 4.Is 26486 divisible by 5?
  5. 5.Is 23978 divisible by 10?
  6. 6.Is 124574 divisible by 23?
  7. 7.Is 15456 divisible by 8?
  8. 8.Is 34498 divisible by 7?
  9. 9.Is 7257 divisible by 10?
  10. 10.Is 11876 divisible by 4?
  11. 11.Is 13919 divisible by 9?
  12. 12.Is 82703 divisible by 15?
  13. 13.Is 10810 divisible by 6?
  14. 14.Is 11666 divisible by 12?
  15. 15.Is 6060 divisible by 4?
  16. 16.Is 48546 divisible by 29?
  17. 17.Is 104076 divisible by 18?
  18. 18.Is 53603 divisible by 8?
  19. 19.Is 49880 divisible by 29?
  20. 20.Is 9423 divisible by 3?
  21. 21.Is 3536 divisible by 3?
  22. 22.Is 139640 divisible by 20?
  23. 23.Is 84420 divisible by 15?
  24. 24.Is 35371 divisible by 13?
  25. 25.Is 1095 divisible by 3?
  26. 26.Is 105236 divisible by 17?
  27. 27.Is 112820 divisible by 20?
  28. 28.Is 39063 divisible by 29?
  29. 29.Is 11518 divisible by 13?
  30. 30.Is 40392 divisible by 6?
  31. 31.Is 91569 divisible by 29?
  32. 32.Is 13596 divisible by 5?
  33. 33.Is 119989 divisible by 30?
  34. 34.Is 3262 divisible by 2?
  35. 35.Is 41976 divisible by 6?
  36. 36.Is 62845 divisible by 9?
  37. 37.Is 1038 divisible by 6?
  38. 38.Is 3381 divisible by 7?
  39. 39.Is 87950 divisible by 15?
  40. 40.Is 41730 divisible by 23?

Answer key

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

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