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Divisibility Rules Worksheet

Vedic maths trick 13: Divisibility tests · Set 135 · 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 19663 divisible by 7?
  2. 2.Is 11142 divisible by 7?
  3. 3.Is 100470 divisible by 15?
  4. 4.Is 59102 divisible by 29?
  5. 5.Is 64830 divisible by 30?
  6. 6.Is 2897 divisible by 13?
  7. 7.Is 7470 divisible by 30?
  8. 8.Is 9542 divisible by 11?
  9. 9.Is 71193 divisible by 13?
  10. 10.Is 28370 divisible by 17?
  11. 11.Is 13039 divisible by 13?
  12. 12.Is 11286 divisible by 19?
  13. 13.Is 16840 divisible by 9?
  14. 14.Is 18024 divisible by 8?
  15. 15.Is 4327 divisible by 2?
  16. 16.Is 19509 divisible by 7?
  17. 17.Is 4232 divisible by 4?
  18. 18.Is 117967 divisible by 23?
  19. 19.Is 52991 divisible by 8?
  20. 20.Is 92950 divisible by 15?
  21. 21.Is 10802 divisible by 18?
  22. 22.Is 62612 divisible by 11?
  23. 23.Is 1656 divisible by 6?
  24. 24.Is 19785 divisible by 3?
  25. 25.Is 17501 divisible by 5?
  26. 26.Is 10430 divisible by 6?
  27. 27.Is 9757 divisible by 17?
  28. 28.Is 48515 divisible by 8?
  29. 29.Is 104782 divisible by 19?
  30. 30.Is 18620 divisible by 4?
  31. 31.Is 12839 divisible by 17?
  32. 32.Is 6220 divisible by 9?
  33. 33.Is 44627 divisible by 20?
  34. 34.Is 39234 divisible by 19?
  35. 35.Is 13773 divisible by 4?
  36. 36.Is 79087 divisible by 29?
  37. 37.Is 52632 divisible by 18?
  38. 38.Is 2095 divisible by 19?
  39. 39.Is 9156 divisible by 2?
  40. 40.Is 16051 divisible by 7?

Answer key

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

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