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Divisibility Rules Worksheet

Vedic maths trick 13: Divisibility tests · Set 691 · 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 72199 divisible by 23?
  2. 2.Is 179830 divisible by 30?
  3. 3.Is 12319 divisible by 2?
  4. 4.Is 18730 divisible by 3?
  5. 5.Is 95046 divisible by 15?
  6. 6.Is 26417 divisible by 4?
  7. 7.Is 21758 divisible by 23?
  8. 8.Is 385 divisible by 3?
  9. 9.Is 37476 divisible by 12?
  10. 10.Is 19092 divisible by 3?
  11. 11.Is 19809 divisible by 3?
  12. 12.Is 79081 divisible by 29?
  13. 13.Is 70007 divisible by 10?
  14. 14.Is 19741 divisible by 19?
  15. 15.Is 110952 divisible by 24?
  16. 16.Is 74472 divisible by 12?
  17. 17.Is 7392 divisible by 24?
  18. 18.Is 17578 divisible by 29?
  19. 19.Is 68762 divisible by 29?
  20. 20.Is 3324 divisible by 7?
  21. 21.Is 93888 divisible by 18?
  22. 22.Is 31230 divisible by 15?
  23. 23.Is 74172 divisible by 23?
  24. 24.Is 43605 divisible by 15?
  25. 25.Is 40205 divisible by 7?
  26. 26.Is 38737 divisible by 15?
  27. 27.Is 119436 divisible by 29?
  28. 28.Is 2576 divisible by 23?
  29. 29.Is 31948 divisible by 5?
  30. 30.Is 130310 divisible by 30?
  31. 31.Is 75009 divisible by 11?
  32. 32.Is 52791 divisible by 12?
  33. 33.Is 8409 divisible by 3?
  34. 34.Is 8492 divisible by 9?
  35. 35.Is 61860 divisible by 15?
  36. 36.Is 26752 divisible by 11?
  37. 37.Is 6720 divisible by 6?
  38. 38.Is 3200 divisible by 9?
  39. 39.Is 72722 divisible by 13?
  40. 40.Is 48662 divisible by 15?

Answer key

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

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