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Divisibility Rules Worksheet

Vedic maths trick 13: Divisibility tests · Set 366 · 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 26511 divisible by 29?
  2. 2.Is 5104 divisible by 11?
  3. 3.Is 78316 divisible by 30?
  4. 4.Is 100221 divisible by 15?
  5. 5.Is 3896 divisible by 17?
  6. 6.Is 14161 divisible by 5?
  7. 7.Is 36036 divisible by 6?
  8. 8.Is 55125 divisible by 9?
  9. 9.Is 129839 divisible by 20?
  10. 10.Is 42540 divisible by 15?
  11. 11.Is 75130 divisible by 11?
  12. 12.Is 117575 divisible by 20?
  13. 13.Is 35594 divisible by 13?
  14. 14.Is 121011 divisible by 19?
  15. 15.Is 192360 divisible by 30?
  16. 16.Is 18563 divisible by 17?
  17. 17.Is 106172 divisible by 24?
  18. 18.Is 10384 divisible by 8?
  19. 19.Is 115092 divisible by 18?
  20. 20.Is 13632 divisible by 8?
  21. 21.Is 2945 divisible by 19?
  22. 22.Is 5926 divisible by 24?
  23. 23.Is 129276 divisible by 19?
  24. 24.Is 8202 divisible by 10?
  25. 25.Is 21523 divisible by 12?
  26. 26.Is 5660 divisible by 6?
  27. 27.Is 165622 divisible by 24?
  28. 28.Is 85151 divisible by 30?
  29. 29.Is 5100 divisible by 5?
  30. 30.Is 101443 divisible by 17?
  31. 31.Is 9716 divisible by 6?
  32. 32.Is 113965 divisible by 23?
  33. 33.Is 19304 divisible by 8?
  34. 34.Is 59102 divisible by 29?
  35. 35.Is 148118 divisible by 30?
  36. 36.Is 29354 divisible by 15?
  37. 37.Is 60675 divisible by 15?
  38. 38.Is 50856 divisible by 8?
  39. 39.Is 12600 divisible by 10?
  40. 40.Is 167836 divisible by 29?

Answer key

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

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