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Divisibility Rules Worksheet

Vedic maths trick 13: Divisibility tests · Set 860 · 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 31295 divisible by 5?
  2. 2.Is 39973 divisible by 11?
  3. 3.Is 23040 divisible by 5?
  4. 4.Is 9119 divisible by 2?
  5. 5.Is 1110 divisible by 18?
  6. 6.Is 4222 divisible by 4?
  7. 7.Is 9563 divisible by 3?
  8. 8.Is 104747 divisible by 24?
  9. 9.Is 267 divisible by 2?
  10. 10.Is 77432 divisible by 18?
  11. 11.Is 3592 divisible by 3?
  12. 12.Is 5644 divisible by 4?
  13. 13.Is 13714 divisible by 2?
  14. 14.Is 623 divisible by 4?
  15. 15.Is 168600 divisible by 30?
  16. 16.Is 3256 divisible by 11?
  17. 17.Is 59064 divisible by 24?
  18. 18.Is 8657 divisible by 2?
  19. 19.Is 43204 divisible by 7?
  20. 20.Is 17358 divisible by 11?
  21. 21.Is 8548 divisible by 8?
  22. 22.Is 1068 divisible by 12?
  23. 23.Is 80231 divisible by 17?
  24. 24.Is 18292 divisible by 15?
  25. 25.Is 97485 divisible by 15?
  26. 26.Is 38797 divisible by 12?
  27. 27.Is 22907 divisible by 19?
  28. 28.Is 46334 divisible by 18?
  29. 29.Is 752 divisible by 4?
  30. 30.Is 40484 divisible by 29?
  31. 31.Is 1398 divisible by 2?
  32. 32.Is 25184 divisible by 8?
  33. 33.Is 23653 divisible by 11?
  34. 34.Is 1885 divisible by 29?
  35. 35.Is 65616 divisible by 18?
  36. 36.Is 14582 divisible by 20?
  37. 37.Is 72659 divisible by 19?
  38. 38.Is 21560 divisible by 4?
  39. 39.Is 22000 divisible by 4?
  40. 40.Is 23868 divisible by 17?

Answer key

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

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