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Divisibility Rules Worksheet

Vedic maths trick 13: Divisibility tests · Set 47 · 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 19247 divisible by 10?
  2. 2.Is 8648 divisible by 2?
  3. 3.Is 142530 divisible by 30?
  4. 4.Is 22108 divisible by 4?
  5. 5.Is 7834 divisible by 11?
  6. 6.Is 35209 divisible by 12?
  7. 7.Is 38027 divisible by 11?
  8. 8.Is 55440 divisible by 12?
  9. 9.Is 75378 divisible by 17?
  10. 10.Is 53697 divisible by 13?
  11. 11.Is 13172 divisible by 3?
  12. 12.Is 30287 divisible by 30?
  13. 13.Is 17309 divisible by 19?
  14. 14.Is 14791 divisible by 9?
  15. 15.Is 13504 divisible by 2?
  16. 16.Is 1935 divisible by 2?
  17. 17.Is 32487 divisible by 19?
  18. 18.Is 10139 divisible by 2?
  19. 19.Is 131460 divisible by 20?
  20. 20.Is 2627 divisible by 4?
  21. 21.Is 34645 divisible by 12?
  22. 22.Is 153755 divisible by 23?
  23. 23.Is 35070 divisible by 6?
  24. 24.Is 48355 divisible by 19?
  25. 25.Is 40138 divisible by 7?
  26. 26.Is 36642 divisible by 17?
  27. 27.Is 31509 divisible by 10?
  28. 28.Is 91820 divisible by 29?
  29. 29.Is 54961 divisible by 13?
  30. 30.Is 48760 divisible by 23?
  31. 31.Is 64461 divisible by 15?
  32. 32.Is 25799 divisible by 15?
  33. 33.Is 73337 divisible by 11?
  34. 34.Is 32448 divisible by 13?
  35. 35.Is 30448 divisible by 19?
  36. 36.Is 11568 divisible by 3?
  37. 37.Is 22300 divisible by 20?
  38. 38.Is 66675 divisible by 24?
  39. 39.Is 7288 divisible by 6?
  40. 40.Is 17365 divisible by 23?

Answer key

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

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