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Divisibility Rules Worksheet

Vedic maths trick 13: Divisibility tests · Set 913 · 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 19656 divisible by 3?
  2. 2.Is 23598 divisible by 9?
  3. 3.Is 14251 divisible by 4?
  4. 4.Is 34492 divisible by 10?
  5. 5.Is 54711 divisible by 9?
  6. 6.Is 84423 divisible by 15?
  7. 7.Is 11267 divisible by 4?
  8. 8.Is 7580 divisible by 4?
  9. 9.Is 2973 divisible by 6?
  10. 10.Is 114653 divisible by 18?
  11. 11.Is 209460 divisible by 30?
  12. 12.Is 15077 divisible by 4?
  13. 13.Is 22808 divisible by 4?
  14. 14.Is 25265 divisible by 5?
  15. 15.Is 53273 divisible by 29?
  16. 16.Is 20774 divisible by 4?
  17. 17.Is 1942 divisible by 3?
  18. 18.Is 32850 divisible by 6?
  19. 19.Is 11051 divisible by 2?
  20. 20.Is 13748 divisible by 5?
  21. 21.Is 42630 divisible by 13?
  22. 22.Is 50375 divisible by 13?
  23. 23.Is 25047 divisible by 4?
  24. 24.Is 59859 divisible by 9?
  25. 25.Is 66605 divisible by 11?
  26. 26.Is 16555 divisible by 7?
  27. 27.Is 16437 divisible by 3?
  28. 28.Is 22179 divisible by 13?
  29. 29.Is 103872 divisible by 24?
  30. 30.Is 105858 divisible by 18?
  31. 31.Is 46920 divisible by 30?
  32. 32.Is 71105 divisible by 30?
  33. 33.Is 55167 divisible by 24?
  34. 34.Is 43476 divisible by 18?
  35. 35.Is 3048 divisible by 24?
  36. 36.Is 31646 divisible by 12?
  37. 37.Is 16920 divisible by 15?
  38. 38.Is 76700 divisible by 20?
  39. 39.Is 32450 divisible by 10?
  40. 40.Is 56180 divisible by 24?

Answer key

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

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