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Divisibility Rules Worksheet

Vedic maths trick 13: Divisibility tests · Set 530 · 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 60457 divisible by 9?
  2. 2.Is 77912 divisible by 12?
  3. 3.Is 8184 divisible by 3?
  4. 4.Is 10697 divisible by 2?
  5. 5.Is 80316 divisible by 23?
  6. 6.Is 24954 divisible by 29?
  7. 7.Is 22016 divisible by 6?
  8. 8.Is 32977 divisible by 10?
  9. 9.Is 18187 divisible by 11?
  10. 10.Is 40420 divisible by 10?
  11. 11.Is 151415 divisible by 30?
  12. 12.Is 2604 divisible by 4?
  13. 13.Is 2256 divisible by 4?
  14. 14.Is 4148 divisible by 23?
  15. 15.Is 61409 divisible by 13?
  16. 16.Is 5074 divisible by 15?
  17. 17.Is 10770 divisible by 5?
  18. 18.Is 12360 divisible by 13?
  19. 19.Is 41132 divisible by 20?
  20. 20.Is 8613 divisible by 11?
  21. 21.Is 13692 divisible by 4?
  22. 22.Is 5867 divisible by 7?
  23. 23.Is 32708 divisible by 17?
  24. 24.Is 75780 divisible by 20?
  25. 25.Is 61106 divisible by 12?
  26. 26.Is 107312 divisible by 19?
  27. 27.Is 63297 divisible by 24?
  28. 28.Is 40075 divisible by 7?
  29. 29.Is 30114 divisible by 7?
  30. 30.Is 1267 divisible by 4?
  31. 31.Is 85565 divisible by 20?
  32. 32.Is 41248 divisible by 8?
  33. 33.Is 42952 divisible by 8?
  34. 34.Is 2943 divisible by 2?
  35. 35.Is 10362 divisible by 6?
  36. 36.Is 29542 divisible by 12?
  37. 37.Is 2106 divisible by 5?
  38. 38.Is 58540 divisible by 20?
  39. 39.Is 5260 divisible by 2?
  40. 40.Is 90610 divisible by 13?

Answer key

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

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