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Divisibility Rules Worksheet

Vedic maths trick 13: Divisibility tests · Set 948 · 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 96765 divisible by 15?
  2. 2.Is 118381 divisible by 23?
  3. 3.Is 32087 divisible by 20?
  4. 4.Is 116995 divisible by 29?
  5. 5.Is 9128 divisible by 8?
  6. 6.Is 6024 divisible by 12?
  7. 7.Is 42166 divisible by 29?
  8. 8.Is 10963 divisible by 2?
  9. 9.Is 11630 divisible by 5?
  10. 10.Is 31980 divisible by 12?
  11. 11.Is 55424 divisible by 9?
  12. 12.Is 2301 divisible by 2?
  13. 13.Is 8855 divisible by 11?
  14. 14.Is 13176 divisible by 3?
  15. 15.Is 58863 divisible by 10?
  16. 16.Is 22451 divisible by 12?
  17. 17.Is 701 divisible by 3?
  18. 18.Is 29345 divisible by 5?
  19. 19.Is 77010 divisible by 15?
  20. 20.Is 2529 divisible by 4?
  21. 21.Is 1319 divisible by 2?
  22. 22.Is 7329 divisible by 7?
  23. 23.Is 78910 divisible by 13?
  24. 24.Is 17445 divisible by 5?
  25. 25.Is 94384 divisible by 17?
  26. 26.Is 186330 divisible by 30?
  27. 27.Is 46066 divisible by 9?
  28. 28.Is 33353 divisible by 11?
  29. 29.Is 4004 divisible by 7?
  30. 30.Is 24588 divisible by 6?
  31. 31.Is 18003 divisible by 7?
  32. 32.Is 32563 divisible by 20?
  33. 33.Is 2408 divisible by 4?
  34. 34.Is 35856 divisible by 24?
  35. 35.Is 11804 divisible by 13?
  36. 36.Is 22359 divisible by 4?
  37. 37.Is 15515 divisible by 10?
  38. 38.Is 58825 divisible by 20?
  39. 39.Is 11166 divisible by 2?
  40. 40.Is 58311 divisible by 9?

Answer key

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

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