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Divisibility Rules Worksheet

Vedic maths trick 13: Divisibility tests · Set 611 · 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 14766 divisible by 23?
  2. 2.Is 152047 divisible by 29?
  3. 3.Is 73260 divisible by 18?
  4. 4.Is 28523 divisible by 6?
  5. 5.Is 3140 divisible by 20?
  6. 6.Is 11603 divisible by 9?
  7. 7.Is 35397 divisible by 6?
  8. 8.Is 5137 divisible by 24?
  9. 9.Is 25934 divisible by 9?
  10. 10.Is 11147 divisible by 6?
  11. 11.Is 136340 divisible by 20?
  12. 12.Is 79174 divisible by 12?
  13. 13.Is 78560 divisible by 17?
  14. 14.Is 16655 divisible by 9?
  15. 15.Is 14874 divisible by 18?
  16. 16.Is 31753 divisible by 5?
  17. 17.Is 21060 divisible by 12?
  18. 18.Is 27235 divisible by 6?
  19. 19.Is 8056 divisible by 4?
  20. 20.Is 60034 divisible by 13?
  21. 21.Is 102225 divisible by 29?
  22. 22.Is 4935 divisible by 4?
  23. 23.Is 60920 divisible by 10?
  24. 24.Is 4711 divisible by 7?
  25. 25.Is 7861 divisible by 10?
  26. 26.Is 17794 divisible by 4?
  27. 27.Is 22256 divisible by 13?
  28. 28.Is 39007 divisible by 23?
  29. 29.Is 48296 divisible by 8?
  30. 30.Is 3163 divisible by 17?
  31. 31.Is 6768 divisible by 20?
  32. 32.Is 19327 divisible by 8?
  33. 33.Is 11451 divisible by 11?
  34. 34.Is 48739 divisible by 20?
  35. 35.Is 1979 divisible by 2?
  36. 36.Is 69772 divisible by 11?
  37. 37.Is 12724 divisible by 5?
  38. 38.Is 1447 divisible by 2?
  39. 39.Is 36190 divisible by 10?
  40. 40.Is 114183 divisible by 24?

Answer key

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

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