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Divisibility Rules Worksheet

Vedic maths trick 13: Divisibility tests · Set 892 · 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 24059 divisible by 23?
  2. 2.Is 25018 divisible by 7?
  3. 3.Is 16003 divisible by 3?
  4. 4.Is 7314 divisible by 6?
  5. 5.Is 157056 divisible by 24?
  6. 6.Is 46902 divisible by 24?
  7. 7.Is 16695 divisible by 29?
  8. 8.Is 94530 divisible by 30?
  9. 9.Is 18040 divisible by 10?
  10. 10.Is 21551 divisible by 11?
  11. 11.Is 113999 divisible by 24?
  12. 12.Is 113778 divisible by 20?
  13. 13.Is 60776 divisible by 13?
  14. 14.Is 47333 divisible by 9?
  15. 15.Is 140820 divisible by 30?
  16. 16.Is 57158 divisible by 30?
  17. 17.Is 826 divisible by 20?
  18. 18.Is 17575 divisible by 5?
  19. 19.Is 7042 divisible by 8?
  20. 20.Is 16563 divisible by 3?
  21. 21.Is 20995 divisible by 5?
  22. 22.Is 134712 divisible by 24?
  23. 23.Is 100640 divisible by 20?
  24. 24.Is 8733 divisible by 3?
  25. 25.Is 92300 divisible by 23?
  26. 26.Is 97264 divisible by 15?
  27. 27.Is 25174 divisible by 4?
  28. 28.Is 134421 divisible by 24?
  29. 29.Is 16208 divisible by 8?
  30. 30.Is 4118 divisible by 4?
  31. 31.Is 65987 divisible by 17?
  32. 32.Is 68750 divisible by 11?
  33. 33.Is 28195 divisible by 5?
  34. 34.Is 67716 divisible by 18?
  35. 35.Is 40992 divisible by 24?
  36. 36.Is 6286 divisible by 2?
  37. 37.Is 10439 divisible by 4?
  38. 38.Is 65482 divisible by 13?
  39. 39.Is 111621 divisible by 29?
  40. 40.Is 42440 divisible by 20?

Answer key

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

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