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Divisibility Rules Worksheet

Vedic maths trick 13: Divisibility tests · Set 689 · 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 76703 divisible by 23?
  2. 2.Is 10452 divisible by 13?
  3. 3.Is 28098 divisible by 5?
  4. 4.Is 65656 divisible by 29?
  5. 5.Is 17159 divisible by 8?
  6. 6.Is 5903 divisible by 7?
  7. 7.Is 19702 divisible by 6?
  8. 8.Is 61299 divisible by 9?
  9. 9.Is 31904 divisible by 12?
  10. 10.Is 9154 divisible by 23?
  11. 11.Is 56572 divisible by 23?
  12. 12.Is 68218 divisible by 23?
  13. 13.Is 73536 divisible by 11?
  14. 14.Is 67313 divisible by 17?
  15. 15.Is 8803 divisible by 2?
  16. 16.Is 78752 divisible by 23?
  17. 17.Is 54032 divisible by 17?
  18. 18.Is 89400 divisible by 17?
  19. 19.Is 3132 divisible by 18?
  20. 20.Is 61204 divisible by 11?
  21. 21.Is 9597 divisible by 12?
  22. 22.Is 81846 divisible by 18?
  23. 23.Is 10691 divisible by 20?
  24. 24.Is 185790 divisible by 30?
  25. 25.Is 25614 divisible by 6?
  26. 26.Is 15896 divisible by 12?
  27. 27.Is 19230 divisible by 6?
  28. 28.Is 5553 divisible by 3?
  29. 29.Is 15239 divisible by 20?
  30. 30.Is 18835 divisible by 8?
  31. 31.Is 75976 divisible by 11?
  32. 32.Is 43317 divisible by 9?
  33. 33.Is 83076 divisible by 12?
  34. 34.Is 2560 divisible by 20?
  35. 35.Is 1755 divisible by 13?
  36. 36.Is 50474 divisible by 9?
  37. 37.Is 3060 divisible by 17?
  38. 38.Is 39809 divisible by 11?
  39. 39.Is 87057 divisible by 17?
  40. 40.Is 47861 divisible by 8?

Answer key

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

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