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Divisibility Rules Worksheet

Vedic maths trick 13: Divisibility tests · Set 23 · 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 15689 divisible by 12?
  2. 2.Is 18105 divisible by 3?
  3. 3.Is 5953 divisible by 2?
  4. 4.Is 5663 divisible by 29?
  5. 5.Is 45266 divisible by 13?
  6. 6.Is 25104 divisible by 5?
  7. 7.Is 131871 divisible by 29?
  8. 8.Is 5902 divisible by 4?
  9. 9.Is 18229 divisible by 4?
  10. 10.Is 19424 divisible by 4?
  11. 11.Is 11096 divisible by 19?
  12. 12.Is 76095 divisible by 15?
  13. 13.Is 32500 divisible by 10?
  14. 14.Is 9313 divisible by 3?
  15. 15.Is 24839 divisible by 8?
  16. 16.Is 31736 divisible by 8?
  17. 17.Is 2033 divisible by 2?
  18. 18.Is 43120 divisible by 7?
  19. 19.Is 37732 divisible by 7?
  20. 20.Is 166054 divisible by 29?
  21. 21.Is 12517 divisible by 4?
  22. 22.Is 252 divisible by 2?
  23. 23.Is 87244 divisible by 17?
  24. 24.Is 4870 divisible by 4?
  25. 25.Is 44495 divisible by 11?
  26. 26.Is 21406 divisible by 7?
  27. 27.Is 102306 divisible by 17?
  28. 28.Is 21750 divisible by 15?
  29. 29.Is 15188 divisible by 9?
  30. 30.Is 23425 divisible by 7?
  31. 31.Is 9884 divisible by 2?
  32. 32.Is 478 divisible by 2?
  33. 33.Is 427 divisible by 7?
  34. 34.Is 1659 divisible by 3?
  35. 35.Is 6389 divisible by 6?
  36. 36.Is 58506 divisible by 20?
  37. 37.Is 102649 divisible by 24?
  38. 38.Is 27708 divisible by 8?
  39. 39.Is 13920 divisible by 4?
  40. 40.Is 36351 divisible by 12?

Answer key

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

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