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Divisibility Rules Worksheet

Vedic maths trick 13: Divisibility tests · Set 368 · 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 133139 divisible by 29?
  2. 2.Is 29237 divisible by 7?
  3. 3.Is 69955 divisible by 15?
  4. 4.Is 47866 divisible by 7?
  5. 5.Is 14332 divisible by 4?
  6. 6.Is 14000 divisible by 10?
  7. 7.Is 1916 divisible by 2?
  8. 8.Is 26526 divisible by 12?
  9. 9.Is 1618 divisible by 17?
  10. 10.Is 68865 divisible by 15?
  11. 11.Is 91164 divisible by 15?
  12. 12.Is 20238 divisible by 6?
  13. 13.Is 39027 divisible by 23?
  14. 14.Is 8579 divisible by 3?
  15. 15.Is 125327 divisible by 29?
  16. 16.Is 2590 divisible by 7?
  17. 17.Is 108342 divisible by 18?
  18. 18.Is 26472 divisible by 12?
  19. 19.Is 5697 divisible by 9?
  20. 20.Is 75475 divisible by 12?
  21. 21.Is 59371 divisible by 20?
  22. 22.Is 173913 divisible by 29?
  23. 23.Is 32420 divisible by 20?
  24. 24.Is 40996 divisible by 24?
  25. 25.Is 7452 divisible by 3?
  26. 26.Is 10572 divisible by 2?
  27. 27.Is 11707 divisible by 10?
  28. 28.Is 9298 divisible by 13?
  29. 29.Is 13741 divisible by 5?
  30. 30.Is 28879 divisible by 5?
  31. 31.Is 26124 divisible by 12?
  32. 32.Is 27780 divisible by 4?
  33. 33.Is 67920 divisible by 24?
  34. 34.Is 66952 divisible by 17?
  35. 35.Is 35567 divisible by 9?
  36. 36.Is 195510 divisible by 30?
  37. 37.Is 83400 divisible by 12?
  38. 38.Is 42987 divisible by 23?
  39. 39.Is 3187 divisible by 2?
  40. 40.Is 47047 divisible by 12?

Answer key

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

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