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Divisibility Rules Worksheet

Vedic maths trick 13: Divisibility tests · Set 387 · 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 8911 divisible by 4?
  2. 2.Is 16443 divisible by 13?
  3. 3.Is 48435 divisible by 15?
  4. 4.Is 6695 divisible by 4?
  5. 5.Is 126464 divisible by 29?
  6. 6.Is 3648 divisible by 12?
  7. 7.Is 2712 divisible by 10?
  8. 8.Is 57570 divisible by 15?
  9. 9.Is 1011 divisible by 3?
  10. 10.Is 26160 divisible by 15?
  11. 11.Is 31640 divisible by 23?
  12. 12.Is 2838 divisible by 15?
  13. 13.Is 12819 divisible by 29?
  14. 14.Is 28700 divisible by 7?
  15. 15.Is 29232 divisible by 9?
  16. 16.Is 59891 divisible by 17?
  17. 17.Is 943 divisible by 4?
  18. 18.Is 45069 divisible by 8?
  19. 19.Is 154561 divisible by 23?
  20. 20.Is 35703 divisible by 7?
  21. 21.Is 111186 divisible by 29?
  22. 22.Is 63380 divisible by 10?
  23. 23.Is 21783 divisible by 4?
  24. 24.Is 47772 divisible by 12?
  25. 25.Is 8875 divisible by 2?
  26. 26.Is 50020 divisible by 17?
  27. 27.Is 3993 divisible by 7?
  28. 28.Is 67017 divisible by 15?
  29. 29.Is 3813 divisible by 3?
  30. 30.Is 150990 divisible by 30?
  31. 31.Is 55841 divisible by 10?
  32. 32.Is 135246 divisible by 30?
  33. 33.Is 4593 divisible by 7?
  34. 34.Is 45878 divisible by 7?
  35. 35.Is 13378 divisible by 4?
  36. 36.Is 17907 divisible by 3?
  37. 37.Is 5482 divisible by 7?
  38. 38.Is 20380 divisible by 20?
  39. 39.Is 22588 divisible by 4?
  40. 40.Is 46091 divisible by 9?

Answer key

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

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