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Divisibility Rules Worksheet

Vedic maths trick 13: Divisibility tests · Set 688 · 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 100089 divisible by 18?
  2. 2.Is 37854 divisible by 18?
  3. 3.Is 180438 divisible by 29?
  4. 4.Is 8791 divisible by 4?
  5. 5.Is 1604 divisible by 11?
  6. 6.Is 57333 divisible by 17?
  7. 7.Is 4461 divisible by 3?
  8. 8.Is 37919 divisible by 7?
  9. 9.Is 127138 divisible by 19?
  10. 10.Is 73877 divisible by 11?
  11. 11.Is 6951 divisible by 2?
  12. 12.Is 3703 divisible by 23?
  13. 13.Is 51228 divisible by 12?
  14. 14.Is 4689 divisible by 3?
  15. 15.Is 65205 divisible by 13?
  16. 16.Is 5661 divisible by 3?
  17. 17.Is 9933 divisible by 3?
  18. 18.Is 52635 divisible by 15?
  19. 19.Is 203259 divisible by 30?
  20. 20.Is 91032 divisible by 29?
  21. 21.Is 187305 divisible by 30?
  22. 22.Is 13567 divisible by 2?
  23. 23.Is 38754 divisible by 10?
  24. 24.Is 45200 divisible by 20?
  25. 25.Is 18235 divisible by 9?
  26. 26.Is 42111 divisible by 9?
  27. 27.Is 8013 divisible by 12?
  28. 28.Is 33605 divisible by 9?
  29. 29.Is 116514 divisible by 18?
  30. 30.Is 76879 divisible by 11?
  31. 31.Is 16836 divisible by 3?
  32. 32.Is 109840 divisible by 20?
  33. 33.Is 96930 divisible by 30?
  34. 34.Is 68364 divisible by 11?
  35. 35.Is 11210 divisible by 19?
  36. 36.Is 58715 divisible by 12?
  37. 37.Is 9482 divisible by 10?
  38. 38.Is 40072 divisible by 8?
  39. 39.Is 15058 divisible by 24?
  40. 40.Is 19456 divisible by 4?

Answer key

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

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