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Divisibility Rules Worksheet

Vedic maths trick 13: Divisibility tests · Set 976 · 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 79411 divisible by 13?
  2. 2.Is 68816 divisible by 11?
  3. 3.Is 30742 divisible by 10?
  4. 4.Is 70259 divisible by 24?
  5. 5.Is 49732 divisible by 20?
  6. 6.Is 75863 divisible by 12?
  7. 7.Is 40971 divisible by 17?
  8. 8.Is 80649 divisible by 29?
  9. 9.Is 46874 divisible by 23?
  10. 10.Is 9520 divisible by 7?
  11. 11.Is 133645 divisible by 30?
  12. 12.Is 28175 divisible by 6?
  13. 13.Is 1898 divisible by 5?
  14. 14.Is 15211 divisible by 3?
  15. 15.Is 35264 divisible by 19?
  16. 16.Is 14678 divisible by 6?
  17. 17.Is 55890 divisible by 10?
  18. 18.Is 14464 divisible by 3?
  19. 19.Is 26244 divisible by 4?
  20. 20.Is 13259 divisible by 3?
  21. 21.Is 124668 divisible by 24?
  22. 22.Is 104234 divisible by 19?
  23. 23.Is 52164 divisible by 9?
  24. 24.Is 61948 divisible by 12?
  25. 25.Is 14221 divisible by 6?
  26. 26.Is 118643 divisible by 17?
  27. 27.Is 80940 divisible by 19?
  28. 28.Is 3874 divisible by 9?
  29. 29.Is 27523 divisible by 12?
  30. 30.Is 189690 divisible by 29?
  31. 31.Is 75622 divisible by 20?
  32. 32.Is 7042 divisible by 2?
  33. 33.Is 83293 divisible by 23?
  34. 34.Is 1025 divisible by 18?
  35. 35.Is 11099 divisible by 2?
  36. 36.Is 1521 divisible by 2?
  37. 37.Is 34276 divisible by 11?
  38. 38.Is 27368 divisible by 11?
  39. 39.Is 62491 divisible by 11?
  40. 40.Is 6610 divisible by 6?

Answer key

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

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