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Divisibility Rules Worksheet

Vedic maths trick 13: Divisibility tests · Set 889 · 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 94627 divisible by 23?
  2. 2.Is 17145 divisible by 9?
  3. 3.Is 41211 divisible by 9?
  4. 4.Is 9981 divisible by 2?
  5. 5.Is 11192 divisible by 2?
  6. 6.Is 15468 divisible by 4?
  7. 7.Is 106627 divisible by 24?
  8. 8.Is 30162 divisible by 11?
  9. 9.Is 19720 divisible by 5?
  10. 10.Is 46152 divisible by 18?
  11. 11.Is 100678 divisible by 17?
  12. 12.Is 26917 divisible by 20?
  13. 13.Is 117131 divisible by 29?
  14. 14.Is 67887 divisible by 19?
  15. 15.Is 58 divisible by 3?
  16. 16.Is 119831 divisible by 24?
  17. 17.Is 53104 divisible by 8?
  18. 18.Is 47320 divisible by 20?
  19. 19.Is 23161 divisible by 9?
  20. 20.Is 22393 divisible by 12?
  21. 21.Is 108870 divisible by 17?
  22. 22.Is 4214 divisible by 13?
  23. 23.Is 20884 divisible by 7?
  24. 24.Is 10639 divisible by 2?
  25. 25.Is 13831 divisible by 6?
  26. 26.Is 39540 divisible by 30?
  27. 27.Is 67683 divisible by 11?
  28. 28.Is 44877 divisible by 10?
  29. 29.Is 17336 divisible by 9?
  30. 30.Is 5815 divisible by 4?
  31. 31.Is 165396 divisible by 30?
  32. 32.Is 17231 divisible by 5?
  33. 33.Is 72768 divisible by 17?
  34. 34.Is 32989 divisible by 6?
  35. 35.Is 101897 divisible by 19?
  36. 36.Is 37869 divisible by 13?
  37. 37.Is 40338 divisible by 6?
  38. 38.Is 44448 divisible by 30?
  39. 39.Is 56259 divisible by 9?
  40. 40.Is 206105 divisible by 30?

Answer key

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

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