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Divisibility Rules Worksheet

Vedic maths trick 13: Divisibility tests · Set 295 · 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 121452 divisible by 29?
  2. 2.Is 867 divisible by 2?
  3. 3.Is 405 divisible by 15?
  4. 4.Is 14574 divisible by 9?
  5. 5.Is 119654 divisible by 29?
  6. 6.Is 4021 divisible by 3?
  7. 7.Is 91723 divisible by 18?
  8. 8.Is 33160 divisible by 8?
  9. 9.Is 40007 divisible by 11?
  10. 10.Is 86019 divisible by 23?
  11. 11.Is 1884 divisible by 4?
  12. 12.Is 14728 divisible by 4?
  13. 13.Is 100355 divisible by 19?
  14. 14.Is 63622 divisible by 13?
  15. 15.Is 124080 divisible by 20?
  16. 16.Is 56817 divisible by 9?
  17. 17.Is 27318 divisible by 11?
  18. 18.Is 46930 divisible by 13?
  19. 19.Is 680 divisible by 17?
  20. 20.Is 35845 divisible by 12?
  21. 21.Is 38523 divisible by 20?
  22. 22.Is 49529 divisible by 11?
  23. 23.Is 108425 divisible by 23?
  24. 24.Is 50060 divisible by 8?
  25. 25.Is 109813 divisible by 18?
  26. 26.Is 137610 divisible by 30?
  27. 27.Is 3082 divisible by 7?
  28. 28.Is 48180 divisible by 15?
  29. 29.Is 52071 divisible by 17?
  30. 30.Is 105270 divisible by 29?
  31. 31.Is 33248 divisible by 29?
  32. 32.Is 8666 divisible by 8?
  33. 33.Is 37210 divisible by 13?
  34. 34.Is 6840 divisible by 20?
  35. 35.Is 94190 divisible by 29?
  36. 36.Is 22244 divisible by 5?
  37. 37.Is 8115 divisible by 9?
  38. 38.Is 113158 divisible by 29?
  39. 39.Is 9859 divisible by 4?
  40. 40.Is 12104 divisible by 5?

Answer key

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

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