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Divisibility Rules Worksheet

Vedic maths trick 13: Divisibility tests · Set 473 · 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 7164 divisible by 2?
  2. 2.Is 20320 divisible by 8?
  3. 3.Is 58487 divisible by 30?
  4. 4.Is 121148 divisible by 20?
  5. 5.Is 24713 divisible by 4?
  6. 6.Is 4769 divisible by 4?
  7. 7.Is 47838 divisible by 20?
  8. 8.Is 8104 divisible by 3?
  9. 9.Is 30276 divisible by 6?
  10. 10.Is 33928 divisible by 8?
  11. 11.Is 26746 divisible by 9?
  12. 12.Is 4652 divisible by 7?
  13. 13.Is 7807 divisible by 3?
  14. 14.Is 12927 divisible by 3?
  15. 15.Is 17509 divisible by 13?
  16. 16.Is 25727 divisible by 9?
  17. 17.Is 16847 divisible by 4?
  18. 18.Is 3060 divisible by 30?
  19. 19.Is 19030 divisible by 6?
  20. 20.Is 31660 divisible by 19?
  21. 21.Is 17027 divisible by 19?
  22. 22.Is 163740 divisible by 30?
  23. 23.Is 115371 divisible by 19?
  24. 24.Is 29764 divisible by 7?
  25. 25.Is 82127 divisible by 19?
  26. 26.Is 26992 divisible by 15?
  27. 27.Is 6040 divisible by 7?
  28. 28.Is 2170 divisible by 6?
  29. 29.Is 17088 divisible by 3?
  30. 30.Is 26128 divisible by 12?
  31. 31.Is 63371 divisible by 11?
  32. 32.Is 29488 divisible by 8?
  33. 33.Is 10919 divisible by 6?
  34. 34.Is 5366 divisible by 2?
  35. 35.Is 29931 divisible by 23?
  36. 36.Is 34702 divisible by 8?
  37. 37.Is 8047 divisible by 13?
  38. 38.Is 12873 divisible by 4?
  39. 39.Is 40440 divisible by 30?
  40. 40.Is 19979 divisible by 3?

Answer key

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

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