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Divisibility Rules Worksheet

Vedic maths trick 13: Divisibility tests · Set 399 · 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 101993 divisible by 18?
  2. 2.Is 4747 divisible by 20?
  3. 3.Is 11049 divisible by 2?
  4. 4.Is 4804 divisible by 2?
  5. 5.Is 30168 divisible by 18?
  6. 6.Is 64114 divisible by 11?
  7. 7.Is 70226 divisible by 15?
  8. 8.Is 23394 divisible by 7?
  9. 9.Is 111069 divisible by 20?
  10. 10.Is 15540 divisible by 10?
  11. 11.Is 47241 divisible by 9?
  12. 12.Is 105582 divisible by 19?
  13. 13.Is 13798 divisible by 3?
  14. 14.Is 110700 divisible by 20?
  15. 15.Is 191370 divisible by 30?
  16. 16.Is 15276 divisible by 10?
  17. 17.Is 34190 divisible by 9?
  18. 18.Is 44867 divisible by 11?
  19. 19.Is 14466 divisible by 6?
  20. 20.Is 116859 divisible by 18?
  21. 21.Is 38070 divisible by 10?
  22. 22.Is 35419 divisible by 11?
  23. 23.Is 19089 divisible by 6?
  24. 24.Is 30079 divisible by 7?
  25. 25.Is 42895 divisible by 23?
  26. 26.Is 14901 divisible by 3?
  27. 27.Is 13349 divisible by 4?
  28. 28.Is 87348 divisible by 24?
  29. 29.Is 73285 divisible by 20?
  30. 30.Is 52382 divisible by 9?
  31. 31.Is 46926 divisible by 7?
  32. 32.Is 52731 divisible by 9?
  33. 33.Is 3878 divisible by 5?
  34. 34.Is 10717 divisible by 11?
  35. 35.Is 1500 divisible by 4?
  36. 36.Is 87243 divisible by 13?
  37. 37.Is 10868 divisible by 3?
  38. 38.Is 36517 divisible by 13?
  39. 39.Is 107647 divisible by 30?
  40. 40.Is 31938 divisible by 8?

Answer key

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

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