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Divisibility Rules Worksheet

Vedic maths trick 13: Divisibility tests · Set 436 · 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 3129 divisible by 4?
  2. 2.Is 82820 divisible by 17?
  3. 3.Is 118469 divisible by 20?
  4. 4.Is 901 divisible by 4?
  5. 5.Is 3589 divisible by 18?
  6. 6.Is 31860 divisible by 12?
  7. 7.Is 60896 divisible by 13?
  8. 8.Is 87094 divisible by 20?
  9. 9.Is 53460 divisible by 10?
  10. 10.Is 41580 divisible by 11?
  11. 11.Is 6952 divisible by 17?
  12. 12.Is 9471 divisible by 7?
  13. 13.Is 17059 divisible by 7?
  14. 14.Is 10831 divisible by 23?
  15. 15.Is 52657 divisible by 8?
  16. 16.Is 177090 divisible by 29?
  17. 17.Is 60747 divisible by 18?
  18. 18.Is 61810 divisible by 10?
  19. 19.Is 122835 divisible by 19?
  20. 20.Is 111883 divisible by 19?
  21. 21.Is 11799 divisible by 5?
  22. 22.Is 61161 divisible by 18?
  23. 23.Is 83110 divisible by 19?
  24. 24.Is 3604 divisible by 3?
  25. 25.Is 33492 divisible by 6?
  26. 26.Is 21013 divisible by 4?
  27. 27.Is 4845 divisible by 2?
  28. 28.Is 39742 divisible by 13?
  29. 29.Is 35517 divisible by 7?
  30. 30.Is 10130 divisible by 5?
  31. 31.Is 109041 divisible by 19?
  32. 32.Is 16419 divisible by 4?
  33. 33.Is 45108 divisible by 7?
  34. 34.Is 27371 divisible by 30?
  35. 35.Is 53556 divisible by 12?
  36. 36.Is 25369 divisible by 19?
  37. 37.Is 132445 divisible by 20?
  38. 38.Is 18065 divisible by 5?
  39. 39.Is 27368 divisible by 4?
  40. 40.Is 105843 divisible by 23?

Answer key

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

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