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Divisibility Rules Worksheet

Vedic maths trick 13: Divisibility tests · Set 637 · 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 69930 divisible by 18?
  2. 2.Is 1236 divisible by 3?
  3. 3.Is 8927 divisible by 18?
  4. 4.Is 36418 divisible by 7?
  5. 5.Is 128832 divisible by 24?
  6. 6.Is 67682 divisible by 10?
  7. 7.Is 40359 divisible by 11?
  8. 8.Is 130525 divisible by 23?
  9. 9.Is 1130 divisible by 6?
  10. 10.Is 37769 divisible by 8?
  11. 11.Is 81765 divisible by 23?
  12. 12.Is 39781 divisible by 9?
  13. 13.Is 20924 divisible by 4?
  14. 14.Is 4829 divisible by 4?
  15. 15.Is 13110 divisible by 4?
  16. 16.Is 60186 divisible by 20?
  17. 17.Is 22813 divisible by 6?
  18. 18.Is 37453 divisible by 13?
  19. 19.Is 32314 divisible by 10?
  20. 20.Is 52205 divisible by 8?
  21. 21.Is 14295 divisible by 15?
  22. 22.Is 181563 divisible by 30?
  23. 23.Is 79475 divisible by 19?
  24. 24.Is 9409 divisible by 6?
  25. 25.Is 3357 divisible by 2?
  26. 26.Is 27092 divisible by 13?
  27. 27.Is 11248 divisible by 3?
  28. 28.Is 55787 divisible by 12?
  29. 29.Is 37207 divisible by 30?
  30. 30.Is 193197 divisible by 30?
  31. 31.Is 29261 divisible by 19?
  32. 32.Is 860 divisible by 5?
  33. 33.Is 54048 divisible by 8?
  34. 34.Is 79982 divisible by 17?
  35. 35.Is 128416 divisible by 19?
  36. 36.Is 76846 divisible by 17?
  37. 37.Is 53376 divisible by 18?
  38. 38.Is 108153 divisible by 18?
  39. 39.Is 27240 divisible by 8?
  40. 40.Is 33425 divisible by 5?

Answer key

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

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