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Divisibility Rules Worksheet

Vedic maths trick 13: Divisibility tests · Set 476 · 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 116093 divisible by 17?
  2. 2.Is 155 divisible by 10?
  3. 3.Is 8036 divisible by 2?
  4. 4.Is 93035 divisible by 23?
  5. 5.Is 128260 divisible by 20?
  6. 6.Is 7791 divisible by 7?
  7. 7.Is 44184 divisible by 12?
  8. 8.Is 17952 divisible by 12?
  9. 9.Is 11764 divisible by 17?
  10. 10.Is 60120 divisible by 24?
  11. 11.Is 20180 divisible by 4?
  12. 12.Is 8894 divisible by 6?
  13. 13.Is 25897 divisible by 29?
  14. 14.Is 16920 divisible by 20?
  15. 15.Is 53277 divisible by 13?
  16. 16.Is 73946 divisible by 13?
  17. 17.Is 113518 divisible by 18?
  18. 18.Is 2936 divisible by 8?
  19. 19.Is 128859 divisible by 24?
  20. 20.Is 18171 divisible by 12?
  21. 21.Is 109744 divisible by 19?
  22. 22.Is 46638 divisible by 10?
  23. 23.Is 157642 divisible by 23?
  24. 24.Is 78768 divisible by 24?
  25. 25.Is 17316 divisible by 4?
  26. 26.Is 19117 divisible by 3?
  27. 27.Is 5462 divisible by 7?
  28. 28.Is 189399 divisible by 29?
  29. 29.Is 93861 divisible by 15?
  30. 30.Is 8654 divisible by 7?
  31. 31.Is 4867 divisible by 7?
  32. 32.Is 18527 divisible by 5?
  33. 33.Is 38145 divisible by 15?
  34. 34.Is 15518 divisible by 5?
  35. 35.Is 49036 divisible by 23?
  36. 36.Is 20605 divisible by 5?
  37. 37.Is 34314 divisible by 19?
  38. 38.Is 103439 divisible by 19?
  39. 39.Is 19990 divisible by 5?
  40. 40.Is 14337 divisible by 8?

Answer key

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

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