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Divisibility Rules Worksheet

Vedic maths trick 13: Divisibility tests · Set 817 · 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 38569 divisible by 10?
  2. 2.Is 40684 divisible by 11?
  3. 3.Is 121140 divisible by 30?
  4. 4.Is 32757 divisible by 8?
  5. 5.Is 25040 divisible by 4?
  6. 6.Is 2534 divisible by 5?
  7. 7.Is 102429 divisible by 29?
  8. 8.Is 19071 divisible by 11?
  9. 9.Is 30427 divisible by 11?
  10. 10.Is 12375 divisible by 11?
  11. 11.Is 29197 divisible by 7?
  12. 12.Is 10440 divisible by 29?
  13. 13.Is 1634 divisible by 4?
  14. 14.Is 35453 divisible by 11?
  15. 15.Is 7668 divisible by 23?
  16. 16.Is 91589 divisible by 24?
  17. 17.Is 66769 divisible by 15?
  18. 18.Is 48875 divisible by 17?
  19. 19.Is 15757 divisible by 7?
  20. 20.Is 82280 divisible by 20?
  21. 21.Is 25361 divisible by 23?
  22. 22.Is 116190 divisible by 30?
  23. 23.Is 41756 divisible by 11?
  24. 24.Is 140537 divisible by 30?
  25. 25.Is 21075 divisible by 12?
  26. 26.Is 4346 divisible by 6?
  27. 27.Is 4336 divisible by 4?
  28. 28.Is 104861 divisible by 19?
  29. 29.Is 73080 divisible by 24?
  30. 30.Is 10783 divisible by 11?
  31. 31.Is 39254 divisible by 9?
  32. 32.Is 5785 divisible by 5?
  33. 33.Is 11220 divisible by 24?
  34. 34.Is 31693 divisible by 20?
  35. 35.Is 6205 divisible by 7?
  36. 36.Is 75225 divisible by 29?
  37. 37.Is 25697 divisible by 7?
  38. 38.Is 6321 divisible by 8?
  39. 39.Is 5544 divisible by 6?
  40. 40.Is 48135 divisible by 24?

Answer key

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

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