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Divisibility Rules Worksheet

Vedic maths trick 13: Divisibility tests · Set 807 · 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 5734 divisible by 11?
  2. 2.Is 5810 divisible by 5?
  3. 3.Is 6670 divisible by 4?
  4. 4.Is 40392 divisible by 8?
  5. 5.Is 62419 divisible by 12?
  6. 6.Is 10624 divisible by 8?
  7. 7.Is 46286 divisible by 15?
  8. 8.Is 133469 divisible by 30?
  9. 9.Is 57285 divisible by 15?
  10. 10.Is 555 divisible by 15?
  11. 11.Is 442 divisible by 13?
  12. 12.Is 124645 divisible by 23?
  13. 13.Is 18840 divisible by 9?
  14. 14.Is 41420 divisible by 10?
  15. 15.Is 89737 divisible by 13?
  16. 16.Is 10803 divisible by 4?
  17. 17.Is 20284 divisible by 3?
  18. 18.Is 71296 divisible by 18?
  19. 19.Is 135061 divisible by 20?
  20. 20.Is 30420 divisible by 20?
  21. 21.Is 68527 divisible by 18?
  22. 22.Is 12865 divisible by 4?
  23. 23.Is 91677 divisible by 18?
  24. 24.Is 15784 divisible by 8?
  25. 25.Is 4977 divisible by 7?
  26. 26.Is 10738 divisible by 7?
  27. 27.Is 119489 divisible by 23?
  28. 28.Is 2815 divisible by 2?
  29. 29.Is 123639 divisible by 29?
  30. 30.Is 2472 divisible by 2?
  31. 31.Is 153015 divisible by 24?
  32. 32.Is 4438 divisible by 7?
  33. 33.Is 109245 divisible by 18?
  34. 34.Is 87240 divisible by 20?
  35. 35.Is 73321 divisible by 17?
  36. 36.Is 33630 divisible by 15?
  37. 37.Is 17653 divisible by 6?
  38. 38.Is 141317 divisible by 29?
  39. 39.Is 14503 divisible by 6?
  40. 40.Is 8701 divisible by 4?

Answer key

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

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