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Divisibility Rules Worksheet

Vedic maths trick 13: Divisibility tests · Set 837 · 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 93305 divisible by 17?
  2. 2.Is 23852 divisible by 8?
  3. 3.Is 10176 divisible by 4?
  4. 4.Is 34752 divisible by 8?
  5. 5.Is 5952 divisible by 2?
  6. 6.Is 66801 divisible by 15?
  7. 7.Is 57844 divisible by 30?
  8. 8.Is 9476 divisible by 2?
  9. 9.Is 44297 divisible by 20?
  10. 10.Is 25968 divisible by 4?
  11. 11.Is 62320 divisible by 19?
  12. 12.Is 34242 divisible by 13?
  13. 13.Is 9558 divisible by 6?
  14. 14.Is 53052 divisible by 8?
  15. 15.Is 39276 divisible by 9?
  16. 16.Is 88780 divisible by 23?
  17. 17.Is 3496 divisible by 6?
  18. 18.Is 40868 divisible by 11?
  19. 19.Is 10619 divisible by 18?
  20. 20.Is 65189 divisible by 19?
  21. 21.Is 119242 divisible by 19?
  22. 22.Is 7767 divisible by 5?
  23. 23.Is 116073 divisible by 19?
  24. 24.Is 11975 divisible by 6?
  25. 25.Is 10642 divisible by 2?
  26. 26.Is 4992 divisible by 13?
  27. 27.Is 95880 divisible by 17?
  28. 28.Is 10830 divisible by 10?
  29. 29.Is 10520 divisible by 20?
  30. 30.Is 108643 divisible by 20?
  31. 31.Is 14400 divisible by 8?
  32. 32.Is 32256 divisible by 9?
  33. 33.Is 2330 divisible by 2?
  34. 34.Is 29535 divisible by 15?
  35. 35.Is 61548 divisible by 23?
  36. 36.Is 8706 divisible by 3?
  37. 37.Is 52514 divisible by 11?
  38. 38.Is 23256 divisible by 4?
  39. 39.Is 15587 divisible by 9?
  40. 40.Is 109138 divisible by 19?

Answer key

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

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