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Divisibility Rules Worksheet

Vedic maths trick 13: Divisibility tests · Set 148 · 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 15233 divisible by 10?
  2. 2.Is 6575 divisible by 18?
  3. 3.Is 5520 divisible by 10?
  4. 4.Is 162515 divisible by 30?
  5. 5.Is 6135 divisible by 3?
  6. 6.Is 48552 divisible by 12?
  7. 7.Is 16968 divisible by 3?
  8. 8.Is 17323 divisible by 6?
  9. 9.Is 8010 divisible by 10?
  10. 10.Is 116794 divisible by 23?
  11. 11.Is 10206 divisible by 2?
  12. 12.Is 26802 divisible by 6?
  13. 13.Is 47310 divisible by 7?
  14. 14.Is 64106 divisible by 19?
  15. 15.Is 48840 divisible by 12?
  16. 16.Is 206250 divisible by 30?
  17. 17.Is 15288 divisible by 4?
  18. 18.Is 8309 divisible by 4?
  19. 19.Is 23905 divisible by 4?
  20. 20.Is 46457 divisible by 18?
  21. 21.Is 20530 divisible by 10?
  22. 22.Is 43283 divisible by 23?
  23. 23.Is 25891 divisible by 8?
  24. 24.Is 11129 divisible by 13?
  25. 25.Is 108866 divisible by 17?
  26. 26.Is 8020 divisible by 2?
  27. 27.Is 16667 divisible by 29?
  28. 28.Is 88704 divisible by 24?
  29. 29.Is 3664 divisible by 8?
  30. 30.Is 51595 divisible by 8?
  31. 31.Is 144762 divisible by 23?
  32. 32.Is 51804 divisible by 9?
  33. 33.Is 63014 divisible by 13?
  34. 34.Is 137661 divisible by 23?
  35. 35.Is 27966 divisible by 6?
  36. 36.Is 42648 divisible by 12?
  37. 37.Is 26450 divisible by 5?
  38. 38.Is 34004 divisible by 6?
  39. 39.Is 14115 divisible by 4?
  40. 40.Is 39136 divisible by 17?

Answer key

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

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