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Divisibility Rules Worksheet

Vedic maths trick 13: Divisibility tests · Set 963 · 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 93976 divisible by 17?
  2. 2.Is 27765 divisible by 8?
  3. 3.Is 27377 divisible by 7?
  4. 4.Is 24152 divisible by 4?
  5. 5.Is 23437 divisible by 20?
  6. 6.Is 26629 divisible by 4?
  7. 7.Is 21737 divisible by 12?
  8. 8.Is 2574 divisible by 3?
  9. 9.Is 83772 divisible by 15?
  10. 10.Is 91230 divisible by 15?
  11. 11.Is 1744 divisible by 2?
  12. 12.Is 30170 divisible by 7?
  13. 13.Is 4031 divisible by 2?
  14. 14.Is 5506 divisible by 2?
  15. 15.Is 51588 divisible by 12?
  16. 16.Is 14984 divisible by 4?
  17. 17.Is 9088 divisible by 8?
  18. 18.Is 29313 divisible by 9?
  19. 19.Is 139316 divisible by 29?
  20. 20.Is 47802 divisible by 9?
  21. 21.Is 29260 divisible by 11?
  22. 22.Is 69360 divisible by 12?
  23. 23.Is 85307 divisible by 23?
  24. 24.Is 74701 divisible by 18?
  25. 25.Is 123804 divisible by 19?
  26. 26.Is 6960 divisible by 8?
  27. 27.Is 78648 divisible by 17?
  28. 28.Is 27047 divisible by 17?
  29. 29.Is 12115 divisible by 3?
  30. 30.Is 6507 divisible by 5?
  31. 31.Is 4405 divisible by 20?
  32. 32.Is 57387 divisible by 13?
  33. 33.Is 2530 divisible by 10?
  34. 34.Is 13205 divisible by 12?
  35. 35.Is 26787 divisible by 17?
  36. 36.Is 63210 divisible by 15?
  37. 37.Is 27295 divisible by 5?
  38. 38.Is 7455 divisible by 7?
  39. 39.Is 57200 divisible by 13?
  40. 40.Is 46655 divisible by 7?

Answer key

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

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