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Divisibility Rules Worksheet

Vedic maths trick 13: Divisibility tests · Set 265 · 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 6423 divisible by 19?
  2. 2.Is 6014 divisible by 2?
  3. 3.Is 44286 divisible by 7?
  4. 4.Is 114648 divisible by 23?
  5. 5.Is 7002 divisible by 18?
  6. 6.Is 15480 divisible by 10?
  7. 7.Is 7368 divisible by 4?
  8. 8.Is 1740 divisible by 15?
  9. 9.Is 43958 divisible by 29?
  10. 10.Is 1756 divisible by 4?
  11. 11.Is 38346 divisible by 6?
  12. 12.Is 4856 divisible by 13?
  13. 13.Is 1150 divisible by 12?
  14. 14.Is 122490 divisible by 30?
  15. 15.Is 3509 divisible by 6?
  16. 16.Is 27363 divisible by 4?
  17. 17.Is 18268 divisible by 3?
  18. 18.Is 64296 divisible by 10?
  19. 19.Is 47331 divisible by 9?
  20. 20.Is 86428 divisible by 17?
  21. 21.Is 15135 divisible by 8?
  22. 22.Is 139961 divisible by 23?
  23. 23.Is 98352 divisible by 18?
  24. 24.Is 19793 divisible by 17?
  25. 25.Is 130400 divisible by 20?
  26. 26.Is 101793 divisible by 15?
  27. 27.Is 102140 divisible by 20?
  28. 28.Is 38855 divisible by 30?
  29. 29.Is 41868 divisible by 7?
  30. 30.Is 54244 divisible by 13?
  31. 31.Is 10007 divisible by 7?
  32. 32.Is 22667 divisible by 6?
  33. 33.Is 2738 divisible by 2?
  34. 34.Is 41532 divisible by 12?
  35. 35.Is 21288 divisible by 12?
  36. 36.Is 10385 divisible by 3?
  37. 37.Is 44387 divisible by 30?
  38. 38.Is 29280 divisible by 17?
  39. 39.Is 114062 divisible by 30?
  40. 40.Is 201936 divisible by 29?

Answer key

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

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