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Divisibility Rules Worksheet

Vedic maths trick 13: Divisibility tests · Set 970 · 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 12903 divisible by 12?
  2. 2.Is 35035 divisible by 7?
  3. 3.Is 2085 divisible by 19?
  4. 4.Is 7979 divisible by 2?
  5. 5.Is 27960 divisible by 6?
  6. 6.Is 105715 divisible by 24?
  7. 7.Is 6826 divisible by 2?
  8. 8.Is 22780 divisible by 4?
  9. 9.Is 29463 divisible by 23?
  10. 10.Is 45564 divisible by 11?
  11. 11.Is 160312 divisible by 29?
  12. 12.Is 185194 divisible by 29?
  13. 13.Is 76978 divisible by 12?
  14. 14.Is 3078 divisible by 9?
  15. 15.Is 36761 divisible by 8?
  16. 16.Is 122400 divisible by 24?
  17. 17.Is 37184 divisible by 7?
  18. 18.Is 158659 divisible by 29?
  19. 19.Is 25080 divisible by 11?
  20. 20.Is 9240 divisible by 3?
  21. 21.Is 11890 divisible by 7?
  22. 22.Is 9541 divisible by 3?
  23. 23.Is 3356 divisible by 3?
  24. 24.Is 37375 divisible by 23?
  25. 25.Is 13398 divisible by 2?
  26. 26.Is 17026 divisible by 8?
  27. 27.Is 74710 divisible by 30?
  28. 28.Is 57060 divisible by 20?
  29. 29.Is 7314 divisible by 3?
  30. 30.Is 28981 divisible by 11?
  31. 31.Is 183120 divisible by 30?
  32. 32.Is 14966 divisible by 7?
  33. 33.Is 14437 divisible by 6?
  34. 34.Is 10139 divisible by 19?
  35. 35.Is 59793 divisible by 10?
  36. 36.Is 42084 divisible by 18?
  37. 37.Is 36727 divisible by 17?
  38. 38.Is 62568 divisible by 12?
  39. 39.Is 104016 divisible by 17?
  40. 40.Is 34580 divisible by 10?

Answer key

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

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