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Divisibility Rules Worksheet

Vedic maths trick 13: Divisibility tests · Set 227 · 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 3312 divisible by 24?
  2. 2.Is 127494 divisible by 19?
  3. 3.Is 14933 divisible by 23?
  4. 4.Is 3375 divisible by 15?
  5. 5.Is 349 divisible by 4?
  6. 6.Is 31212 divisible by 6?
  7. 7.Is 26473 divisible by 15?
  8. 8.Is 1875 divisible by 5?
  9. 9.Is 19880 divisible by 6?
  10. 10.Is 11362 divisible by 2?
  11. 11.Is 19364 divisible by 4?
  12. 12.Is 7263 divisible by 2?
  13. 13.Is 831 divisible by 7?
  14. 14.Is 23700 divisible by 30?
  15. 15.Is 110607 divisible by 23?
  16. 16.Is 14620 divisible by 4?
  17. 17.Is 40373 divisible by 29?
  18. 18.Is 19425 divisible by 20?
  19. 19.Is 66837 divisible by 17?
  20. 20.Is 67940 divisible by 30?
  21. 21.Is 27304 divisible by 8?
  22. 22.Is 48780 divisible by 20?
  23. 23.Is 17431 divisible by 3?
  24. 24.Is 114816 divisible by 23?
  25. 25.Is 79315 divisible by 19?
  26. 26.Is 48300 divisible by 12?
  27. 27.Is 28409 divisible by 29?
  28. 28.Is 22831 divisible by 5?
  29. 29.Is 69350 divisible by 10?
  30. 30.Is 87448 divisible by 17?
  31. 31.Is 22450 divisible by 10?
  32. 32.Is 10544 divisible by 2?
  33. 33.Is 3798 divisible by 10?
  34. 34.Is 41715 divisible by 7?
  35. 35.Is 11644 divisible by 6?
  36. 36.Is 50116 divisible by 12?
  37. 37.Is 52118 divisible by 23?
  38. 38.Is 1716 divisible by 11?
  39. 39.Is 25216 divisible by 8?
  40. 40.Is 47541 divisible by 23?

Answer key

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

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