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Divisibility Rules Worksheet

Vedic maths trick 13: Divisibility tests · Set 771 · 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 34534 divisible by 7?
  2. 2.Is 687 divisible by 23?
  3. 3.Is 82393 divisible by 13?
  4. 4.Is 38312 divisible by 8?
  5. 5.Is 909 divisible by 9?
  6. 6.Is 9436 divisible by 2?
  7. 7.Is 49745 divisible by 11?
  8. 8.Is 2953 divisible by 6?
  9. 9.Is 5162 divisible by 29?
  10. 10.Is 104040 divisible by 17?
  11. 11.Is 993 divisible by 2?
  12. 12.Is 64145 divisible by 20?
  13. 13.Is 8943 divisible by 2?
  14. 14.Is 85324 divisible by 23?
  15. 15.Is 16394 divisible by 6?
  16. 16.Is 1598 divisible by 9?
  17. 17.Is 25023 divisible by 19?
  18. 18.Is 20968 divisible by 3?
  19. 19.Is 11416 divisible by 11?
  20. 20.Is 6350 divisible by 3?
  21. 21.Is 52954 divisible by 29?
  22. 22.Is 15822 divisible by 18?
  23. 23.Is 162542 divisible by 30?
  24. 24.Is 64160 divisible by 20?
  25. 25.Is 36906 divisible by 11?
  26. 26.Is 149999 divisible by 24?
  27. 27.Is 4843 divisible by 2?
  28. 28.Is 19898 divisible by 3?
  29. 29.Is 8674 divisible by 6?
  30. 30.Is 98952 divisible by 24?
  31. 31.Is 30024 divisible by 18?
  32. 32.Is 12081 divisible by 2?
  33. 33.Is 154270 divisible by 23?
  34. 34.Is 121320 divisible by 24?
  35. 35.Is 22908 divisible by 12?
  36. 36.Is 63564 divisible by 12?
  37. 37.Is 25595 divisible by 4?
  38. 38.Is 13982 divisible by 2?
  39. 39.Is 18324 divisible by 6?
  40. 40.Is 33768 divisible by 8?

Answer key

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

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