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Divisibility Rules Worksheet

Vedic maths trick 13: Divisibility tests · Set 66 · 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 138419 divisible by 30?
  2. 2.Is 10319 divisible by 8?
  3. 3.Is 13034 divisible by 12?
  4. 4.Is 96918 divisible by 29?
  5. 5.Is 16879 divisible by 3?
  6. 6.Is 70616 divisible by 19?
  7. 7.Is 138 divisible by 2?
  8. 8.Is 16425 divisible by 10?
  9. 9.Is 37366 divisible by 17?
  10. 10.Is 121770 divisible by 30?
  11. 11.Is 8593 divisible by 4?
  12. 12.Is 3702 divisible by 29?
  13. 13.Is 18658 divisible by 19?
  14. 14.Is 23860 divisible by 5?
  15. 15.Is 54912 divisible by 12?
  16. 16.Is 14309 divisible by 4?
  17. 17.Is 22039 divisible by 15?
  18. 18.Is 47905 divisible by 10?
  19. 19.Is 40196 divisible by 6?
  20. 20.Is 8748 divisible by 6?
  21. 21.Is 44773 divisible by 10?
  22. 22.Is 71256 divisible by 24?
  23. 23.Is 30630 divisible by 6?
  24. 24.Is 87244 divisible by 13?
  25. 25.Is 76368 divisible by 12?
  26. 26.Is 194010 divisible by 29?
  27. 27.Is 24433 divisible by 5?
  28. 28.Is 88784 divisible by 13?
  29. 29.Is 11949 divisible by 2?
  30. 30.Is 6342 divisible by 2?
  31. 31.Is 20728 divisible by 8?
  32. 32.Is 30594 divisible by 29?
  33. 33.Is 25337 divisible by 7?
  34. 34.Is 5185 divisible by 4?
  35. 35.Is 5796 divisible by 7?
  36. 36.Is 74589 divisible by 17?
  37. 37.Is 118161 divisible by 19?
  38. 38.Is 11669 divisible by 7?
  39. 39.Is 179433 divisible by 29?
  40. 40.Is 103333 divisible by 18?

Answer key

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

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