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Divisibility Rules Worksheet

Vedic maths trick 13: Divisibility tests · Set 700 · 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 4749 divisible by 2?
  2. 2.Is 6504 divisible by 24?
  3. 3.Is 34337 divisible by 6?
  4. 4.Is 81085 divisible by 12?
  5. 5.Is 46716 divisible by 12?
  6. 6.Is 18118 divisible by 3?
  7. 7.Is 6522 divisible by 3?
  8. 8.Is 21215 divisible by 10?
  9. 9.Is 59484 divisible by 17?
  10. 10.Is 78680 divisible by 20?
  11. 11.Is 106642 divisible by 17?
  12. 12.Is 103151 divisible by 20?
  13. 13.Is 3780 divisible by 15?
  14. 14.Is 31733 divisible by 10?
  15. 15.Is 48382 divisible by 10?
  16. 16.Is 91920 divisible by 15?
  17. 17.Is 699 divisible by 7?
  18. 18.Is 44090 divisible by 7?
  19. 19.Is 13122 divisible by 5?
  20. 20.Is 17180 divisible by 5?
  21. 21.Is 44350 divisible by 10?
  22. 22.Is 198 divisible by 6?
  23. 23.Is 34121 divisible by 9?
  24. 24.Is 94847 divisible by 17?
  25. 25.Is 59170 divisible by 9?
  26. 26.Is 281 divisible by 3?
  27. 27.Is 32817 divisible by 11?
  28. 28.Is 10032 divisible by 4?
  29. 29.Is 82134 divisible by 18?
  30. 30.Is 30756 divisible by 11?
  31. 31.Is 14910 divisible by 6?
  32. 32.Is 39260 divisible by 20?
  33. 33.Is 10104 divisible by 8?
  34. 34.Is 19366 divisible by 12?
  35. 35.Is 83458 divisible by 30?
  36. 36.Is 7057 divisible by 3?
  37. 37.Is 17073 divisible by 4?
  38. 38.Is 12671 divisible by 8?
  39. 39.Is 2832 divisible by 8?
  40. 40.Is 20577 divisible by 19?

Answer key

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

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