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Divisibility Rules Worksheet

Vedic maths trick 13: Divisibility tests · Set 842 · 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 5716 divisible by 5?
  2. 2.Is 69414 divisible by 18?
  3. 3.Is 93443 divisible by 17?
  4. 4.Is 23553 divisible by 19?
  5. 5.Is 147051 divisible by 29?
  6. 6.Is 37694 divisible by 29?
  7. 7.Is 14587 divisible by 3?
  8. 8.Is 53748 divisible by 18?
  9. 9.Is 3770 divisible by 2?
  10. 10.Is 23140 divisible by 4?
  11. 11.Is 21375 divisible by 5?
  12. 12.Is 120424 divisible by 18?
  13. 13.Is 24978 divisible by 23?
  14. 14.Is 87021 divisible by 29?
  15. 15.Is 11349 divisible by 11?
  16. 16.Is 12793 divisible by 30?
  17. 17.Is 35380 divisible by 10?
  18. 18.Is 138214 divisible by 29?
  19. 19.Is 34294 divisible by 13?
  20. 20.Is 19717 divisible by 10?
  21. 21.Is 4657 divisible by 4?
  22. 22.Is 65991 divisible by 11?
  23. 23.Is 74005 divisible by 23?
  24. 24.Is 143808 divisible by 24?
  25. 25.Is 21471 divisible by 17?
  26. 26.Is 2505 divisible by 3?
  27. 27.Is 40569 divisible by 8?
  28. 28.Is 9432 divisible by 24?
  29. 29.Is 105296 divisible by 19?
  30. 30.Is 6815 divisible by 3?
  31. 31.Is 4673 divisible by 8?
  32. 32.Is 98676 divisible by 30?
  33. 33.Is 23533 divisible by 29?
  34. 34.Is 3960 divisible by 4?
  35. 35.Is 18390 divisible by 15?
  36. 36.Is 18120 divisible by 18?
  37. 37.Is 30040 divisible by 10?
  38. 38.Is 135163 divisible by 20?
  39. 39.Is 92680 divisible by 20?
  40. 40.Is 58977 divisible by 10?

Answer key

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

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