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Divisibility Rules Worksheet

Vedic maths trick 13: Divisibility tests · Set 378 · 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 8745 divisible by 10?
  2. 2.Is 46418 divisible by 12?
  3. 3.Is 5347 divisible by 5?
  4. 4.Is 38108 divisible by 6?
  5. 5.Is 24318 divisible by 7?
  6. 6.Is 70500 divisible by 13?
  7. 7.Is 33150 divisible by 5?
  8. 8.Is 1129 divisible by 4?
  9. 9.Is 15845 divisible by 5?
  10. 10.Is 7668 divisible by 18?
  11. 11.Is 19992 divisible by 4?
  12. 12.Is 5070 divisible by 30?
  13. 13.Is 49305 divisible by 10?
  14. 14.Is 98265 divisible by 15?
  15. 15.Is 3888 divisible by 3?
  16. 16.Is 35274 divisible by 20?
  17. 17.Is 34302 divisible by 6?
  18. 18.Is 10857 divisible by 5?
  19. 19.Is 95070 divisible by 18?
  20. 20.Is 69904 divisible by 11?
  21. 21.Is 7546 divisible by 4?
  22. 22.Is 4006 divisible by 2?
  23. 23.Is 191226 divisible by 29?
  24. 24.Is 121455 divisible by 19?
  25. 25.Is 55646 divisible by 10?
  26. 26.Is 209340 divisible by 30?
  27. 27.Is 31965 divisible by 7?
  28. 28.Is 12307 divisible by 6?
  29. 29.Is 29753 divisible by 5?
  30. 30.Is 8004 divisible by 4?
  31. 31.Is 7371 divisible by 13?
  32. 32.Is 119960 divisible by 18?
  33. 33.Is 128898 divisible by 29?
  34. 34.Is 79114 divisible by 29?
  35. 35.Is 9892 divisible by 4?
  36. 36.Is 21211 divisible by 6?
  37. 37.Is 11930 divisible by 7?
  38. 38.Is 16014 divisible by 4?
  39. 39.Is 57729 divisible by 12?
  40. 40.Is 11920 divisible by 8?

Answer key

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

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