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Divisibility Rules Worksheet

Vedic maths trick 13: Divisibility tests · Set 193 · 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 45423 divisible by 19?
  2. 2.Is 132648 divisible by 19?
  3. 3.Is 139611 divisible by 23?
  4. 4.Is 89874 divisible by 18?
  5. 5.Is 69075 divisible by 15?
  6. 6.Is 4036 divisible by 19?
  7. 7.Is 97182 divisible by 18?
  8. 8.Is 1223 divisible by 3?
  9. 9.Is 3716 divisible by 2?
  10. 10.Is 19145 divisible by 15?
  11. 11.Is 94120 divisible by 20?
  12. 12.Is 106488 divisible by 29?
  13. 13.Is 99232 divisible by 17?
  14. 14.Is 4969 divisible by 5?
  15. 15.Is 42331 divisible by 9?
  16. 16.Is 7315 divisible by 7?
  17. 17.Is 44940 divisible by 7?
  18. 18.Is 14522 divisible by 3?
  19. 19.Is 30492 divisible by 11?
  20. 20.Is 30900 divisible by 20?
  21. 21.Is 17049 divisible by 9?
  22. 22.Is 30096 divisible by 11?
  23. 23.Is 3894 divisible by 5?
  24. 24.Is 10050 divisible by 4?
  25. 25.Is 30319 divisible by 6?
  26. 26.Is 9178 divisible by 13?
  27. 27.Is 1185 divisible by 2?
  28. 28.Is 39330 divisible by 29?
  29. 29.Is 24606 divisible by 19?
  30. 30.Is 8488 divisible by 2?
  31. 31.Is 744 divisible by 3?
  32. 32.Is 21870 divisible by 10?
  33. 33.Is 23868 divisible by 18?
  34. 34.Is 58053 divisible by 30?
  35. 35.Is 9160 divisible by 2?
  36. 36.Is 8525 divisible by 5?
  37. 37.Is 7103 divisible by 5?
  38. 38.Is 61596 divisible by 9?
  39. 39.Is 8344 divisible by 7?
  40. 40.Is 157740 divisible by 30?

Answer key

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

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