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Divisibility Rules Worksheet

Vedic maths trick 13: Divisibility tests · Set 673 · 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 75256 divisible by 23?
  2. 2.Is 43243 divisible by 19?
  3. 3.Is 90321 divisible by 20?
  4. 4.Is 10294 divisible by 2?
  5. 5.Is 69620 divisible by 20?
  6. 6.Is 35778 divisible by 10?
  7. 7.Is 917 divisible by 2?
  8. 8.Is 63187 divisible by 18?
  9. 9.Is 51000 divisible by 10?
  10. 10.Is 60701 divisible by 12?
  11. 11.Is 97444 divisible by 19?
  12. 12.Is 65232 divisible by 18?
  13. 13.Is 14663 divisible by 23?
  14. 14.Is 15016 divisible by 4?
  15. 15.Is 367 divisible by 3?
  16. 16.Is 53216 divisible by 8?
  17. 17.Is 6341 divisible by 2?
  18. 18.Is 54300 divisible by 20?
  19. 19.Is 16329 divisible by 8?
  20. 20.Is 47291 divisible by 17?
  21. 21.Is 25760 divisible by 4?
  22. 22.Is 25896 divisible by 5?
  23. 23.Is 23129 divisible by 8?
  24. 24.Is 54810 divisible by 30?
  25. 25.Is 89320 divisible by 20?
  26. 26.Is 155262 divisible by 23?
  27. 27.Is 29305 divisible by 17?
  28. 28.Is 30634 divisible by 20?
  29. 29.Is 2392 divisible by 4?
  30. 30.Is 8274 divisible by 11?
  31. 31.Is 41027 divisible by 12?
  32. 32.Is 10649 divisible by 8?
  33. 33.Is 40963 divisible by 23?
  34. 34.Is 7446 divisible by 5?
  35. 35.Is 11810 divisible by 2?
  36. 36.Is 6500 divisible by 4?
  37. 37.Is 142883 divisible by 29?
  38. 38.Is 39976 divisible by 7?
  39. 39.Is 161414 divisible by 29?
  40. 40.Is 39637 divisible by 11?

Answer key

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

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