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Divisibility Rules Worksheet

Vedic maths trick 13: Divisibility tests · Set 163 · 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 49042 divisible by 19?
  2. 2.Is 120554 divisible by 29?
  3. 3.Is 58197 divisible by 23?
  4. 4.Is 5321 divisible by 3?
  5. 5.Is 21263 divisible by 4?
  6. 6.Is 5240 divisible by 3?
  7. 7.Is 7670 divisible by 7?
  8. 8.Is 74655 divisible by 15?
  9. 9.Is 19040 divisible by 7?
  10. 10.Is 87021 divisible by 19?
  11. 11.Is 88567 divisible by 19?
  12. 12.Is 14244 divisible by 12?
  13. 13.Is 7472 divisible by 2?
  14. 14.Is 5901 divisible by 3?
  15. 15.Is 49702 divisible by 30?
  16. 16.Is 17901 divisible by 17?
  17. 17.Is 59670 divisible by 17?
  18. 18.Is 78867 divisible by 13?
  19. 19.Is 37589 divisible by 9?
  20. 20.Is 75990 divisible by 17?
  21. 21.Is 45080 divisible by 7?
  22. 22.Is 9720 divisible by 20?
  23. 23.Is 44485 divisible by 7?
  24. 24.Is 23092 divisible by 20?
  25. 25.Is 60710 divisible by 10?
  26. 26.Is 24512 divisible by 4?
  27. 27.Is 15842 divisible by 3?
  28. 28.Is 130084 divisible by 30?
  29. 29.Is 98605 divisible by 23?
  30. 30.Is 109533 divisible by 29?
  31. 31.Is 42621 divisible by 8?
  32. 32.Is 10843 divisible by 3?
  33. 33.Is 18451 divisible by 3?
  34. 34.Is 39663 divisible by 9?
  35. 35.Is 32678 divisible by 10?
  36. 36.Is 42704 divisible by 8?
  37. 37.Is 17341 divisible by 15?
  38. 38.Is 52104 divisible by 24?
  39. 39.Is 37313 divisible by 12?
  40. 40.Is 36808 divisible by 8?

Answer key

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

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