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Divisibility Rules Worksheet

Vedic maths trick 13: Divisibility tests · Set 748 · 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 30601 divisible by 7?
  2. 2.Is 263 divisible by 3?
  3. 3.Is 93799 divisible by 23?
  4. 4.Is 184252 divisible by 29?
  5. 5.Is 95330 divisible by 24?
  6. 6.Is 23821 divisible by 17?
  7. 7.Is 46395 divisible by 7?
  8. 8.Is 31233 divisible by 29?
  9. 9.Is 63655 divisible by 29?
  10. 10.Is 11339 divisible by 2?
  11. 11.Is 30618 divisible by 6?
  12. 12.Is 3288 divisible by 9?
  13. 13.Is 10222 divisible by 2?
  14. 14.Is 50750 divisible by 29?
  15. 15.Is 1122 divisible by 4?
  16. 16.Is 80895 divisible by 20?
  17. 17.Is 35460 divisible by 9?
  18. 18.Is 13828 divisible by 6?
  19. 19.Is 38247 divisible by 6?
  20. 20.Is 39060 divisible by 18?
  21. 21.Is 148319 divisible by 24?
  22. 22.Is 18843 divisible by 11?
  23. 23.Is 3433 divisible by 8?
  24. 24.Is 29055 divisible by 5?
  25. 25.Is 68944 divisible by 11?
  26. 26.Is 25747 divisible by 5?
  27. 27.Is 3817 divisible by 2?
  28. 28.Is 10580 divisible by 23?
  29. 29.Is 29411 divisible by 7?
  30. 30.Is 24300 divisible by 4?
  31. 31.Is 52777 divisible by 17?
  32. 32.Is 65186 divisible by 10?
  33. 33.Is 60930 divisible by 9?
  34. 34.Is 4599 divisible by 2?
  35. 35.Is 1908 divisible by 11?
  36. 36.Is 129086 divisible by 19?
  37. 37.Is 49280 divisible by 10?
  38. 38.Is 36720 divisible by 24?
  39. 39.Is 3942 divisible by 6?
  40. 40.Is 11547 divisible by 8?

Answer key

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

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