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Divisibility Rules Worksheet

Vedic maths trick 13: Divisibility tests · Set 894 · 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 28884 divisible by 23?
  2. 2.Is 15965 divisible by 10?
  3. 3.Is 32348 divisible by 11?
  4. 4.Is 16733 divisible by 11?
  5. 5.Is 90374 divisible by 20?
  6. 6.Is 3234 divisible by 15?
  7. 7.Is 52814 divisible by 8?
  8. 8.Is 6964 divisible by 4?
  9. 9.Is 137852 divisible by 23?
  10. 10.Is 2544 divisible by 23?
  11. 11.Is 2232 divisible by 18?
  12. 12.Is 19123 divisible by 5?
  13. 13.Is 23260 divisible by 4?
  14. 14.Is 18003 divisible by 3?
  15. 15.Is 27070 divisible by 5?
  16. 16.Is 187001 divisible by 30?
  17. 17.Is 2457 divisible by 7?
  18. 18.Is 19810 divisible by 5?
  19. 19.Is 41644 divisible by 9?
  20. 20.Is 4947 divisible by 8?
  21. 21.Is 23950 divisible by 5?
  22. 22.Is 43503 divisible by 17?
  23. 23.Is 108025 divisible by 20?
  24. 24.Is 54700 divisible by 20?
  25. 25.Is 25670 divisible by 9?
  26. 26.Is 24469 divisible by 4?
  27. 27.Is 3240 divisible by 5?
  28. 28.Is 3916 divisible by 19?
  29. 29.Is 34943 divisible by 10?
  30. 30.Is 85034 divisible by 24?
  31. 31.Is 58308 divisible by 9?
  32. 32.Is 12657 divisible by 6?
  33. 33.Is 20955 divisible by 15?
  34. 34.Is 28224 divisible by 8?
  35. 35.Is 49410 divisible by 9?
  36. 36.Is 30876 divisible by 6?
  37. 37.Is 18576 divisible by 5?
  38. 38.Is 74548 divisible by 17?
  39. 39.Is 10605 divisible by 29?
  40. 40.Is 12203 divisible by 2?

Answer key

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

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