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Divisibility Rules Worksheet

Vedic maths trick 13: Divisibility tests · Set 534 · 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 62583 divisible by 20?
  2. 2.Is 9801 divisible by 5?
  3. 3.Is 13616 divisible by 3?
  4. 4.Is 8544 divisible by 3?
  5. 5.Is 154307 divisible by 29?
  6. 6.Is 40560 divisible by 10?
  7. 7.Is 103087 divisible by 24?
  8. 8.Is 29505 divisible by 7?
  9. 9.Is 28531 divisible by 19?
  10. 10.Is 2949 divisible by 2?
  11. 11.Is 12673 divisible by 13?
  12. 12.Is 29337 divisible by 11?
  13. 13.Is 128360 divisible by 30?
  14. 14.Is 33129 divisible by 7?
  15. 15.Is 95073 divisible by 15?
  16. 16.Is 4065 divisible by 6?
  17. 17.Is 101010 divisible by 15?
  18. 18.Is 75840 divisible by 20?
  19. 19.Is 20392 divisible by 6?
  20. 20.Is 72103 divisible by 13?
  21. 21.Is 156009 divisible by 23?
  22. 22.Is 3542 divisible by 11?
  23. 23.Is 41699 divisible by 23?
  24. 24.Is 680 divisible by 20?
  25. 25.Is 123809 divisible by 23?
  26. 26.Is 13823 divisible by 3?
  27. 27.Is 17685 divisible by 9?
  28. 28.Is 67680 divisible by 19?
  29. 29.Is 28008 divisible by 6?
  30. 30.Is 18196 divisible by 5?
  31. 31.Is 72651 divisible by 20?
  32. 32.Is 588 divisible by 3?
  33. 33.Is 19041 divisible by 11?
  34. 34.Is 77600 divisible by 20?
  35. 35.Is 65144 divisible by 23?
  36. 36.Is 1689 divisible by 11?
  37. 37.Is 16413 divisible by 7?
  38. 38.Is 116440 divisible by 20?
  39. 39.Is 3740 divisible by 20?
  40. 40.Is 21409 divisible by 5?

Answer key

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

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