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Divisibility Rules Worksheet

Vedic maths trick 13: Divisibility tests · Set 223 · 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 125889 divisible by 29?
  2. 2.Is 24681 divisible by 19?
  3. 3.Is 61529 divisible by 12?
  4. 4.Is 8966 divisible by 2?
  5. 5.Is 33025 divisible by 7?
  6. 6.Is 28864 divisible by 6?
  7. 7.Is 92310 divisible by 15?
  8. 8.Is 24372 divisible by 19?
  9. 9.Is 4068 divisible by 6?
  10. 10.Is 47674 divisible by 13?
  11. 11.Is 1855 divisible by 5?
  12. 12.Is 646 divisible by 9?
  13. 13.Is 32865 divisible by 5?
  14. 14.Is 10997 divisible by 2?
  15. 15.Is 76764 divisible by 30?
  16. 16.Is 12531 divisible by 4?
  17. 17.Is 7720 divisible by 2?
  18. 18.Is 50188 divisible by 8?
  19. 19.Is 8303 divisible by 20?
  20. 20.Is 47934 divisible by 9?
  21. 21.Is 71334 divisible by 24?
  22. 22.Is 45492 divisible by 17?
  23. 23.Is 25878 divisible by 4?
  24. 24.Is 158856 divisible by 24?
  25. 25.Is 195083 divisible by 29?
  26. 26.Is 44325 divisible by 15?
  27. 27.Is 89910 divisible by 30?
  28. 28.Is 18457 divisible by 24?
  29. 29.Is 54297 divisible by 30?
  30. 30.Is 3577 divisible by 3?
  31. 31.Is 52671 divisible by 9?
  32. 32.Is 13680 divisible by 17?
  33. 33.Is 117283 divisible by 20?
  34. 34.Is 19950 divisible by 5?
  35. 35.Is 32778 divisible by 6?
  36. 36.Is 161352 divisible by 24?
  37. 37.Is 39039 divisible by 11?
  38. 38.Is 9748 divisible by 13?
  39. 39.Is 13466 divisible by 9?
  40. 40.Is 18217 divisible by 9?

Answer key

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

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