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Divisibility Rules Worksheet

Vedic maths trick 13: Divisibility tests · Set 588 · 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 35967 divisible by 19?
  2. 2.Is 15765 divisible by 3?
  3. 3.Is 103877 divisible by 24?
  4. 4.Is 16566 divisible by 15?
  5. 5.Is 42046 divisible by 19?
  6. 6.Is 1918 divisible by 3?
  7. 7.Is 10387 divisible by 19?
  8. 8.Is 15843 divisible by 11?
  9. 9.Is 140544 divisible by 24?
  10. 10.Is 61730 divisible by 10?
  11. 11.Is 80311 divisible by 17?
  12. 12.Is 86345 divisible by 15?
  13. 13.Is 6577 divisible by 10?
  14. 14.Is 37062 divisible by 9?
  15. 15.Is 12420 divisible by 10?
  16. 16.Is 32665 divisible by 5?
  17. 17.Is 65683 divisible by 11?
  18. 18.Is 65198 divisible by 19?
  19. 19.Is 118634 divisible by 23?
  20. 20.Is 11764 divisible by 17?
  21. 21.Is 46944 divisible by 12?
  22. 22.Is 37024 divisible by 13?
  23. 23.Is 43979 divisible by 7?
  24. 24.Is 30102 divisible by 29?
  25. 25.Is 76641 divisible by 11?
  26. 26.Is 11634 divisible by 7?
  27. 27.Is 69333 divisible by 24?
  28. 28.Is 66352 divisible by 13?
  29. 29.Is 35986 divisible by 6?
  30. 30.Is 20622 divisible by 5?
  31. 31.Is 43823 divisible by 29?
  32. 32.Is 35739 divisible by 9?
  33. 33.Is 1424 divisible by 29?
  34. 34.Is 13117 divisible by 13?
  35. 35.Is 114444 divisible by 18?
  36. 36.Is 2585 divisible by 6?
  37. 37.Is 17355 divisible by 15?
  38. 38.Is 13317 divisible by 4?
  39. 39.Is 17508 divisible by 3?
  40. 40.Is 26456 divisible by 4?

Answer key

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

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