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Divisibility Rules Worksheet

Vedic maths trick 13: Divisibility tests · Set 659 · 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 25136 divisible by 8?
  2. 2.Is 33084 divisible by 12?
  3. 3.Is 17148 divisible by 3?
  4. 4.Is 34674 divisible by 6?
  5. 5.Is 4756 divisible by 17?
  6. 6.Is 66413 divisible by 13?
  7. 7.Is 1198 divisible by 2?
  8. 8.Is 31340 divisible by 5?
  9. 9.Is 13960 divisible by 5?
  10. 10.Is 37576 divisible by 7?
  11. 11.Is 49015 divisible by 23?
  12. 12.Is 96407 divisible by 29?
  13. 13.Is 53680 divisible by 11?
  14. 14.Is 14373 divisible by 3?
  15. 15.Is 12236 divisible by 23?
  16. 16.Is 15655 divisible by 18?
  17. 17.Is 15480 divisible by 20?
  18. 18.Is 13632 divisible by 6?
  19. 19.Is 102426 divisible by 19?
  20. 20.Is 7900 divisible by 4?
  21. 21.Is 103797 divisible by 19?
  22. 22.Is 91840 divisible by 17?
  23. 23.Is 14681 divisible by 4?
  24. 24.Is 26880 divisible by 7?
  25. 25.Is 34334 divisible by 23?
  26. 26.Is 13970 divisible by 2?
  27. 27.Is 67119 divisible by 13?
  28. 28.Is 48992 divisible by 17?
  29. 29.Is 191053 divisible by 29?
  30. 30.Is 43080 divisible by 17?
  31. 31.Is 24500 divisible by 5?
  32. 32.Is 31734 divisible by 10?
  33. 33.Is 14502 divisible by 17?
  34. 34.Is 2206 divisible by 2?
  35. 35.Is 43644 divisible by 12?
  36. 36.Is 16792 divisible by 8?
  37. 37.Is 8691 divisible by 6?
  38. 38.Is 15715 divisible by 19?
  39. 39.Is 59742 divisible by 9?
  40. 40.Is 3690 divisible by 6?

Answer key

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

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