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Divisibility Rules Worksheet

Vedic maths trick 13: Divisibility tests · Set 971 · 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 10089 divisible by 9?
  2. 2.Is 133497 divisible by 23?
  3. 3.Is 162574 divisible by 29?
  4. 4.Is 20427 divisible by 3?
  5. 5.Is 4601 divisible by 15?
  6. 6.Is 21126 divisible by 7?
  7. 7.Is 33767 divisible by 5?
  8. 8.Is 93293 divisible by 29?
  9. 9.Is 47000 divisible by 20?
  10. 10.Is 16648 divisible by 4?
  11. 11.Is 112870 divisible by 19?
  12. 12.Is 34980 divisible by 15?
  13. 13.Is 43587 divisible by 29?
  14. 14.Is 7103 divisible by 20?
  15. 15.Is 27406 divisible by 4?
  16. 16.Is 23115 divisible by 6?
  17. 17.Is 52977 divisible by 12?
  18. 18.Is 986 divisible by 17?
  19. 19.Is 11556 divisible by 12?
  20. 20.Is 125533 divisible by 30?
  21. 21.Is 95197 divisible by 23?
  22. 22.Is 7805 divisible by 7?
  23. 23.Is 29505 divisible by 7?
  24. 24.Is 11613 divisible by 2?
  25. 25.Is 17145 divisible by 17?
  26. 26.Is 152950 divisible by 23?
  27. 27.Is 24572 divisible by 12?
  28. 28.Is 7453 divisible by 20?
  29. 29.Is 35948 divisible by 8?
  30. 30.Is 29857 divisible by 7?
  31. 31.Is 63342 divisible by 12?
  32. 32.Is 8491 divisible by 7?
  33. 33.Is 18602 divisible by 29?
  34. 34.Is 15604 divisible by 15?
  35. 35.Is 7248 divisible by 3?
  36. 36.Is 13322 divisible by 2?
  37. 37.Is 50139 divisible by 12?
  38. 38.Is 25229 divisible by 8?
  39. 39.Is 9115 divisible by 5?
  40. 40.Is 9432 divisible by 4?

Answer key

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

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