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Divisibility Rules Worksheet

Vedic maths trick 13: Divisibility tests · Set 106 · 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 34837 divisible by 30?
  2. 2.Is 55168 divisible by 23?
  3. 3.Is 103751 divisible by 30?
  4. 4.Is 24474 divisible by 6?
  5. 5.Is 60556 divisible by 12?
  6. 6.Is 28611 divisible by 11?
  7. 7.Is 24282 divisible by 9?
  8. 8.Is 65401 divisible by 10?
  9. 9.Is 14117 divisible by 19?
  10. 10.Is 96773 divisible by 29?
  11. 11.Is 66837 divisible by 19?
  12. 12.Is 8436 divisible by 3?
  13. 13.Is 75776 divisible by 13?
  14. 14.Is 11384 divisible by 5?
  15. 15.Is 3156 divisible by 2?
  16. 16.Is 26036 divisible by 8?
  17. 17.Is 6011 divisible by 2?
  18. 18.Is 73954 divisible by 11?
  19. 19.Is 9697 divisible by 12?
  20. 20.Is 27792 divisible by 17?
  21. 21.Is 11919 divisible by 23?
  22. 22.Is 24704 divisible by 10?
  23. 23.Is 63439 divisible by 12?
  24. 24.Is 111130 divisible by 17?
  25. 25.Is 94820 divisible by 24?
  26. 26.Is 111920 divisible by 18?
  27. 27.Is 64733 divisible by 19?
  28. 28.Is 78660 divisible by 12?
  29. 29.Is 34800 divisible by 12?
  30. 30.Is 41308 divisible by 10?
  31. 31.Is 21091 divisible by 23?
  32. 32.Is 21565 divisible by 4?
  33. 33.Is 52332 divisible by 29?
  34. 34.Is 36475 divisible by 18?
  35. 35.Is 160515 divisible by 29?
  36. 36.Is 5626 divisible by 2?
  37. 37.Is 10860 divisible by 20?
  38. 38.Is 70324 divisible by 11?
  39. 39.Is 31696 divisible by 8?
  40. 40.Is 21894 divisible by 11?

Answer key

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

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