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Divisibility Rules Worksheet

Vedic maths trick 13: Divisibility tests · Set 757 · 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 24510 divisible by 5?
  2. 2.Is 27078 divisible by 10?
  3. 3.Is 37827 divisible by 23?
  4. 4.Is 13260 divisible by 5?
  5. 5.Is 143764 divisible by 23?
  6. 6.Is 13103 divisible by 3?
  7. 7.Is 117891 divisible by 29?
  8. 8.Is 44586 divisible by 18?
  9. 9.Is 5916 divisible by 3?
  10. 10.Is 20706 divisible by 6?
  11. 11.Is 23241 divisible by 7?
  12. 12.Is 136500 divisible by 30?
  13. 13.Is 147864 divisible by 30?
  14. 14.Is 7488 divisible by 6?
  15. 15.Is 101550 divisible by 24?
  16. 16.Is 22902 divisible by 11?
  17. 17.Is 4073 divisible by 2?
  18. 18.Is 15145 divisible by 3?
  19. 19.Is 7201 divisible by 18?
  20. 20.Is 161820 divisible by 30?
  21. 21.Is 40928 divisible by 7?
  22. 22.Is 42369 divisible by 7?
  23. 23.Is 84905 divisible by 24?
  24. 24.Is 128736 divisible by 24?
  25. 25.Is 48856 divisible by 7?
  26. 26.Is 60225 divisible by 10?
  27. 27.Is 76654 divisible by 24?
  28. 28.Is 23736 divisible by 23?
  29. 29.Is 50405 divisible by 17?
  30. 30.Is 28448 divisible by 13?
  31. 31.Is 1894 divisible by 5?
  32. 32.Is 34915 divisible by 5?
  33. 33.Is 139334 divisible by 23?
  34. 34.Is 55874 divisible by 24?
  35. 35.Is 23761 divisible by 4?
  36. 36.Is 188442 divisible by 29?
  37. 37.Is 157398 divisible by 23?
  38. 38.Is 6672 divisible by 15?
  39. 39.Is 80340 divisible by 15?
  40. 40.Is 25919 divisible by 6?

Answer key

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

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