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Divisibility Rules Worksheet

Vedic maths trick 13: Divisibility tests · Set 786 · 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 104768 divisible by 17?
  2. 2.Is 14488 divisible by 3?
  3. 3.Is 63865 divisible by 18?
  4. 4.Is 17474 divisible by 15?
  5. 5.Is 6312 divisible by 19?
  6. 6.Is 43008 divisible by 24?
  7. 7.Is 45152 divisible by 17?
  8. 8.Is 100376 divisible by 15?
  9. 9.Is 23779 divisible by 6?
  10. 10.Is 72315 divisible by 19?
  11. 11.Is 35446 divisible by 6?
  12. 12.Is 5926 divisible by 3?
  13. 13.Is 14374 divisible by 7?
  14. 14.Is 15127 divisible by 12?
  15. 15.Is 4507 divisible by 4?
  16. 16.Is 65421 divisible by 11?
  17. 17.Is 25365 divisible by 19?
  18. 18.Is 29574 divisible by 18?
  19. 19.Is 11256 divisible by 12?
  20. 20.Is 1009 divisible by 8?
  21. 21.Is 14440 divisible by 8?
  22. 22.Is 6880 divisible by 5?
  23. 23.Is 16971 divisible by 8?
  24. 24.Is 64082 divisible by 12?
  25. 25.Is 17567 divisible by 11?
  26. 26.Is 21418 divisible by 5?
  27. 27.Is 13617 divisible by 4?
  28. 28.Is 4916 divisible by 4?
  29. 29.Is 10020 divisible by 4?
  30. 30.Is 83583 divisible by 15?
  31. 31.Is 20221 divisible by 3?
  32. 32.Is 4416 divisible by 2?
  33. 33.Is 121510 divisible by 29?
  34. 34.Is 52575 divisible by 15?
  35. 35.Is 57336 divisible by 10?
  36. 36.Is 63378 divisible by 12?
  37. 37.Is 24072 divisible by 4?
  38. 38.Is 22740 divisible by 6?
  39. 39.Is 38020 divisible by 20?
  40. 40.Is 10418 divisible by 24?

Answer key

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

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