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Divisibility Rules Worksheet

Vedic maths trick 13: Divisibility tests · Set 441 · 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 4103 divisible by 7?
  2. 2.Is 3306 divisible by 29?
  3. 3.Is 32208 divisible by 8?
  4. 4.Is 12516 divisible by 2?
  5. 5.Is 155711 divisible by 23?
  6. 6.Is 29877 divisible by 23?
  7. 7.Is 42718 divisible by 11?
  8. 8.Is 65262 divisible by 20?
  9. 9.Is 96631 divisible by 30?
  10. 10.Is 19888 divisible by 19?
  11. 11.Is 2476 divisible by 2?
  12. 12.Is 10186 divisible by 8?
  13. 13.Is 54720 divisible by 15?
  14. 14.Is 44885 divisible by 11?
  15. 15.Is 10244 divisible by 4?
  16. 16.Is 90797 divisible by 20?
  17. 17.Is 116705 divisible by 17?
  18. 18.Is 156780 divisible by 30?
  19. 19.Is 26929 divisible by 4?
  20. 20.Is 70389 divisible by 11?
  21. 21.Is 28083 divisible by 23?
  22. 22.Is 63270 divisible by 18?
  23. 23.Is 1033 divisible by 3?
  24. 24.Is 48786 divisible by 7?
  25. 25.Is 5680 divisible by 5?
  26. 26.Is 107267 divisible by 23?
  27. 27.Is 7644 divisible by 7?
  28. 28.Is 7853 divisible by 20?
  29. 29.Is 27682 divisible by 6?
  30. 30.Is 12197 divisible by 7?
  31. 31.Is 19663 divisible by 12?
  32. 32.Is 22816 divisible by 5?
  33. 33.Is 66450 divisible by 15?
  34. 34.Is 18795 divisible by 7?
  35. 35.Is 20680 divisible by 11?
  36. 36.Is 29076 divisible by 15?
  37. 37.Is 945 divisible by 2?
  38. 38.Is 76895 divisible by 13?
  39. 39.Is 23883 divisible by 19?
  40. 40.Is 62642 divisible by 24?

Answer key

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

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