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Divisibility Rules Worksheet

Vedic maths trick 13: Divisibility tests · Set 901 · 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 17106 divisible by 3?
  2. 2.Is 81952 divisible by 19?
  3. 3.Is 14059 divisible by 4?
  4. 4.Is 327 divisible by 11?
  5. 5.Is 21311 divisible by 6?
  6. 6.Is 131642 divisible by 20?
  7. 7.Is 113493 divisible by 17?
  8. 8.Is 28304 divisible by 29?
  9. 9.Is 82456 divisible by 19?
  10. 10.Is 8045 divisible by 6?
  11. 11.Is 139559 divisible by 29?
  12. 12.Is 78096 divisible by 12?
  13. 13.Is 9741 divisible by 8?
  14. 14.Is 137360 divisible by 20?
  15. 15.Is 32988 divisible by 11?
  16. 16.Is 130162 divisible by 23?
  17. 17.Is 88758 divisible by 19?
  18. 18.Is 42074 divisible by 19?
  19. 19.Is 11885 divisible by 17?
  20. 20.Is 25752 divisible by 6?
  21. 21.Is 43368 divisible by 7?
  22. 22.Is 37360 divisible by 18?
  23. 23.Is 53062 divisible by 20?
  24. 24.Is 56660 divisible by 9?
  25. 25.Is 98624 divisible by 23?
  26. 26.Is 9478 divisible by 3?
  27. 27.Is 18129 divisible by 6?
  28. 28.Is 13464 divisible by 4?
  29. 29.Is 52326 divisible by 9?
  30. 30.Is 120180 divisible by 30?
  31. 31.Is 37649 divisible by 11?
  32. 32.Is 20964 divisible by 9?
  33. 33.Is 59356 divisible by 19?
  34. 34.Is 15478 divisible by 5?
  35. 35.Is 132270 divisible by 30?
  36. 36.Is 60434 divisible by 11?
  37. 37.Is 523 divisible by 4?
  38. 38.Is 73476 divisible by 12?
  39. 39.Is 11965 divisible by 2?
  40. 40.Is 5998 divisible by 3?

Answer key

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

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