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Divisibility Rules Worksheet

Vedic maths trick 13: Divisibility tests · Set 169 · 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 38285 divisible by 19?
  2. 2.Is 69600 divisible by 20?
  3. 3.Is 6467 divisible by 3?
  4. 4.Is 5645 divisible by 18?
  5. 5.Is 303 divisible by 2?
  6. 6.Is 5264 divisible by 2?
  7. 7.Is 9911 divisible by 17?
  8. 8.Is 2324 divisible by 3?
  9. 9.Is 50025 divisible by 23?
  10. 10.Is 125886 divisible by 20?
  11. 11.Is 129927 divisible by 24?
  12. 12.Is 20398 divisible by 7?
  13. 13.Is 4026 divisible by 12?
  14. 14.Is 3106 divisible by 2?
  15. 15.Is 160367 divisible by 24?
  16. 16.Is 19657 divisible by 3?
  17. 17.Is 41758 divisible by 8?
  18. 18.Is 202636 divisible by 29?
  19. 19.Is 191516 divisible by 29?
  20. 20.Is 9563 divisible by 10?
  21. 21.Is 129308 divisible by 20?
  22. 22.Is 10118 divisible by 4?
  23. 23.Is 30024 divisible by 24?
  24. 24.Is 53793 divisible by 13?
  25. 25.Is 153907 divisible by 29?
  26. 26.Is 30460 divisible by 5?
  27. 27.Is 33964 divisible by 13?
  28. 28.Is 67391 divisible by 11?
  29. 29.Is 12000 divisible by 5?
  30. 30.Is 58250 divisible by 10?
  31. 31.Is 8602 divisible by 17?
  32. 32.Is 21650 divisible by 4?
  33. 33.Is 9235 divisible by 7?
  34. 34.Is 12418 divisible by 7?
  35. 35.Is 69233 divisible by 13?
  36. 36.Is 7965 divisible by 4?
  37. 37.Is 17552 divisible by 4?
  38. 38.Is 30520 divisible by 20?
  39. 39.Is 59719 divisible by 12?
  40. 40.Is 38441 divisible by 15?

Answer key

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

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