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Divisibility Rules Worksheet

Vedic maths trick 13: Divisibility tests · Set 83 · 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 32820 divisible by 5?
  2. 2.Is 7704 divisible by 3?
  3. 3.Is 18173 divisible by 15?
  4. 4.Is 79895 divisible by 15?
  5. 5.Is 8171 divisible by 6?
  6. 6.Is 38198 divisible by 17?
  7. 7.Is 97350 divisible by 15?
  8. 8.Is 53159 divisible by 17?
  9. 9.Is 81150 divisible by 15?
  10. 10.Is 106374 divisible by 23?
  11. 11.Is 65319 divisible by 17?
  12. 12.Is 10996 divisible by 18?
  13. 13.Is 21886 divisible by 13?
  14. 14.Is 40218 divisible by 8?
  15. 15.Is 58503 divisible by 11?
  16. 16.Is 96165 divisible by 15?
  17. 17.Is 186811 divisible by 30?
  18. 18.Is 53410 divisible by 10?
  19. 19.Is 37885 divisible by 6?
  20. 20.Is 1392 divisible by 6?
  21. 21.Is 150293 divisible by 29?
  22. 22.Is 19919 divisible by 4?
  23. 23.Is 6010 divisible by 2?
  24. 24.Is 12393 divisible by 7?
  25. 25.Is 4659 divisible by 5?
  26. 26.Is 15935 divisible by 29?
  27. 27.Is 22343 divisible by 13?
  28. 28.Is 39647 divisible by 12?
  29. 29.Is 6445 divisible by 7?
  30. 30.Is 49967 divisible by 29?
  31. 31.Is 44319 divisible by 11?
  32. 32.Is 125222 divisible by 29?
  33. 33.Is 12684 divisible by 3?
  34. 34.Is 69170 divisible by 15?
  35. 35.Is 48939 divisible by 11?
  36. 36.Is 57188 divisible by 17?
  37. 37.Is 69207 divisible by 11?
  38. 38.Is 1444 divisible by 19?
  39. 39.Is 11580 divisible by 5?
  40. 40.Is 18272 divisible by 4?

Answer key

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

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