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Divisibility Rules Worksheet

Vedic maths trick 13: Divisibility tests · Set 825 · 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 100023 divisible by 17?
  2. 2.Is 11634 divisible by 17?
  3. 3.Is 24647 divisible by 7?
  4. 4.Is 38203 divisible by 29?
  5. 5.Is 83163 divisible by 19?
  6. 6.Is 69764 divisible by 29?
  7. 7.Is 61500 divisible by 10?
  8. 8.Is 7957 divisible by 6?
  9. 9.Is 59075 divisible by 13?
  10. 10.Is 46732 divisible by 7?
  11. 11.Is 126799 divisible by 23?
  12. 12.Is 16169 divisible by 4?
  13. 13.Is 74723 divisible by 11?
  14. 14.Is 75418 divisible by 17?
  15. 15.Is 134544 divisible by 24?
  16. 16.Is 87280 divisible by 17?
  17. 17.Is 156235 divisible by 30?
  18. 18.Is 84636 divisible by 29?
  19. 19.Is 32748 divisible by 8?
  20. 20.Is 85505 divisible by 20?
  21. 21.Is 33510 divisible by 5?
  22. 22.Is 44220 divisible by 20?
  23. 23.Is 6753 divisible by 4?
  24. 24.Is 18909 divisible by 5?
  25. 25.Is 126384 divisible by 24?
  26. 26.Is 5012 divisible by 17?
  27. 27.Is 26004 divisible by 12?
  28. 28.Is 94848 divisible by 24?
  29. 29.Is 62634 divisible by 13?
  30. 30.Is 28500 divisible by 15?
  31. 31.Is 22215 divisible by 15?
  32. 32.Is 3460 divisible by 3?
  33. 33.Is 38665 divisible by 19?
  34. 34.Is 66454 divisible by 11?
  35. 35.Is 410 divisible by 3?
  36. 36.Is 75327 divisible by 19?
  37. 37.Is 67787 divisible by 12?
  38. 38.Is 6984 divisible by 3?
  39. 39.Is 114549 divisible by 17?
  40. 40.Is 73092 divisible by 20?

Answer key

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

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