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Divisibility Rules Worksheet

Vedic maths trick 13: Divisibility tests · Set 105 · 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 12213 divisible by 4?
  2. 2.Is 76293 divisible by 23?
  3. 3.Is 5291 divisible by 8?
  4. 4.Is 33781 divisible by 9?
  5. 5.Is 48855 divisible by 15?
  6. 6.Is 20020 divisible by 13?
  7. 7.Is 103590 divisible by 18?
  8. 8.Is 18677 divisible by 3?
  9. 9.Is 12095 divisible by 2?
  10. 10.Is 17140 divisible by 5?
  11. 11.Is 9081 divisible by 3?
  12. 12.Is 683 divisible by 2?
  13. 13.Is 26515 divisible by 8?
  14. 14.Is 7499 divisible by 2?
  15. 15.Is 16135 divisible by 7?
  16. 16.Is 35934 divisible by 17?
  17. 17.Is 10805 divisible by 4?
  18. 18.Is 7342 divisible by 6?
  19. 19.Is 182930 divisible by 29?
  20. 20.Is 74672 divisible by 13?
  21. 21.Is 10174 divisible by 6?
  22. 22.Is 50539 divisible by 15?
  23. 23.Is 96373 divisible by 20?
  24. 24.Is 63431 divisible by 18?
  25. 25.Is 24334 divisible by 5?
  26. 26.Is 17372 divisible by 7?
  27. 27.Is 17273 divisible by 19?
  28. 28.Is 34532 divisible by 19?
  29. 29.Is 9942 divisible by 3?
  30. 30.Is 52872 divisible by 8?
  31. 31.Is 21137 divisible by 6?
  32. 32.Is 20619 divisible by 9?
  33. 33.Is 7555 divisible by 5?
  34. 34.Is 36110 divisible by 6?
  35. 35.Is 83263 divisible by 17?
  36. 36.Is 462 divisible by 3?
  37. 37.Is 9979 divisible by 2?
  38. 38.Is 167811 divisible by 29?
  39. 39.Is 125217 divisible by 20?
  40. 40.Is 79117 divisible by 19?

Answer key

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

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