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Divisibility Rules Worksheet

Vedic maths trick 13: Divisibility tests · Set 438 · 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 131918 divisible by 23?
  2. 2.Is 32396 divisible by 6?
  3. 3.Is 16039 divisible by 4?
  4. 4.Is 45216 divisible by 24?
  5. 5.Is 4463 divisible by 3?
  6. 6.Is 484 divisible by 11?
  7. 7.Is 55505 divisible by 20?
  8. 8.Is 8865 divisible by 15?
  9. 9.Is 1092 divisible by 3?
  10. 10.Is 70663 divisible by 13?
  11. 11.Is 21050 divisible by 10?
  12. 12.Is 13542 divisible by 5?
  13. 13.Is 65186 divisible by 11?
  14. 14.Is 31301 divisible by 20?
  15. 15.Is 39708 divisible by 13?
  16. 16.Is 21551 divisible by 13?
  17. 17.Is 17284 divisible by 4?
  18. 18.Is 2606 divisible by 8?
  19. 19.Is 48805 divisible by 7?
  20. 20.Is 27848 divisible by 13?
  21. 21.Is 128250 divisible by 30?
  22. 22.Is 45526 divisible by 7?
  23. 23.Is 11155 divisible by 5?
  24. 24.Is 4431 divisible by 8?
  25. 25.Is 75648 divisible by 12?
  26. 26.Is 30912 divisible by 23?
  27. 27.Is 43902 divisible by 15?
  28. 28.Is 100670 divisible by 24?
  29. 29.Is 25240 divisible by 6?
  30. 30.Is 52067 divisible by 11?
  31. 31.Is 44811 divisible by 13?
  32. 32.Is 73126 divisible by 11?
  33. 33.Is 59410 divisible by 19?
  34. 34.Is 105313 divisible by 20?
  35. 35.Is 25407 divisible by 8?
  36. 36.Is 31588 divisible by 7?
  37. 37.Is 33732 divisible by 18?
  38. 38.Is 5891 divisible by 2?
  39. 39.Is 72732 divisible by 19?
  40. 40.Is 66630 divisible by 15?

Answer key

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

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