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Divisibility Rules Worksheet

Vedic maths trick 13: Divisibility tests · Set 545 · 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 18678 divisible by 4?
  2. 2.Is 58 divisible by 3?
  3. 3.Is 31224 divisible by 24?
  4. 4.Is 71978 divisible by 17?
  5. 5.Is 6972 divisible by 6?
  6. 6.Is 55574 divisible by 11?
  7. 7.Is 111591 divisible by 23?
  8. 8.Is 7788 divisible by 12?
  9. 9.Is 28879 divisible by 10?
  10. 10.Is 79549 divisible by 13?
  11. 11.Is 10087 divisible by 7?
  12. 12.Is 21203 divisible by 13?
  13. 13.Is 70774 divisible by 13?
  14. 14.Is 7969 divisible by 13?
  15. 15.Is 17706 divisible by 3?
  16. 16.Is 28391 divisible by 7?
  17. 17.Is 14748 divisible by 3?
  18. 18.Is 42633 divisible by 11?
  19. 19.Is 53152 divisible by 10?
  20. 20.Is 20120 divisible by 4?
  21. 21.Is 147228 divisible by 23?
  22. 22.Is 16626 divisible by 17?
  23. 23.Is 41060 divisible by 20?
  24. 24.Is 49372 divisible by 10?
  25. 25.Is 6635 divisible by 6?
  26. 26.Is 138591 divisible by 29?
  27. 27.Is 76690 divisible by 18?
  28. 28.Is 252 divisible by 12?
  29. 29.Is 38247 divisible by 19?
  30. 30.Is 94999 divisible by 15?
  31. 31.Is 14018 divisible by 12?
  32. 32.Is 56778 divisible by 13?
  33. 33.Is 59850 divisible by 10?
  34. 34.Is 33572 divisible by 13?
  35. 35.Is 4491 divisible by 7?
  36. 36.Is 1446 divisible by 12?
  37. 37.Is 35900 divisible by 10?
  38. 38.Is 27458 divisible by 15?
  39. 39.Is 19998 divisible by 9?
  40. 40.Is 10696 divisible by 3?

Answer key

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

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