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Divisibility Rules Worksheet

Vedic maths trick 13: Divisibility tests · Set 108 · 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 6593 divisible by 19?
  2. 2.Is 4429 divisible by 4?
  3. 3.Is 95950 divisible by 15?
  4. 4.Is 111520 divisible by 20?
  5. 5.Is 9049 divisible by 18?
  6. 6.Is 105169 divisible by 18?
  7. 7.Is 125520 divisible by 18?
  8. 8.Is 117984 divisible by 17?
  9. 9.Is 110219 divisible by 30?
  10. 10.Is 3619 divisible by 2?
  11. 11.Is 27506 divisible by 17?
  12. 12.Is 79721 divisible by 29?
  13. 13.Is 83503 divisible by 15?
  14. 14.Is 2745 divisible by 2?
  15. 15.Is 5425 divisible by 3?
  16. 16.Is 55155 divisible by 13?
  17. 17.Is 120451 divisible by 23?
  18. 18.Is 36072 divisible by 9?
  19. 19.Is 27390 divisible by 15?
  20. 20.Is 65807 divisible by 17?
  21. 21.Is 30014 divisible by 8?
  22. 22.Is 61170 divisible by 10?
  23. 23.Is 34994 divisible by 19?
  24. 24.Is 38551 divisible by 20?
  25. 25.Is 9213 divisible by 2?
  26. 26.Is 27591 divisible by 4?
  27. 27.Is 86637 divisible by 17?
  28. 28.Is 17361 divisible by 8?
  29. 29.Is 27268 divisible by 12?
  30. 30.Is 114894 divisible by 18?
  31. 31.Is 18395 divisible by 6?
  32. 32.Is 24930 divisible by 5?
  33. 33.Is 11800 divisible by 4?
  34. 34.Is 6652 divisible by 9?
  35. 35.Is 53452 divisible by 29?
  36. 36.Is 25518 divisible by 4?
  37. 37.Is 13449 divisible by 17?
  38. 38.Is 11784 divisible by 5?
  39. 39.Is 81945 divisible by 15?
  40. 40.Is 46838 divisible by 8?

Answer key

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

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