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Divisibility Rules Worksheet

Vedic maths trick 13: Divisibility tests · Set 424 · 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 29960 divisible by 5?
  2. 2.Is 39525 divisible by 6?
  3. 3.Is 98681 divisible by 17?
  4. 4.Is 27977 divisible by 11?
  5. 5.Is 43120 divisible by 10?
  6. 6.Is 2877 divisible by 2?
  7. 7.Is 110162 divisible by 19?
  8. 8.Is 65548 divisible by 11?
  9. 9.Is 193662 divisible by 29?
  10. 10.Is 25704 divisible by 7?
  11. 11.Is 3684 divisible by 4?
  12. 12.Is 40085 divisible by 11?
  13. 13.Is 117275 divisible by 23?
  14. 14.Is 89280 divisible by 24?
  15. 15.Is 17601 divisible by 4?
  16. 16.Is 20250 divisible by 15?
  17. 17.Is 68668 divisible by 24?
  18. 18.Is 39393 divisible by 8?
  19. 19.Is 4759 divisible by 2?
  20. 20.Is 42049 divisible by 7?
  21. 21.Is 58273 divisible by 23?
  22. 22.Is 4417 divisible by 2?
  23. 23.Is 17376 divisible by 12?
  24. 24.Is 35166 divisible by 6?
  25. 25.Is 14384 divisible by 29?
  26. 26.Is 20126 divisible by 29?
  27. 27.Is 69552 divisible by 10?
  28. 28.Is 44263 divisible by 7?
  29. 29.Is 26184 divisible by 12?
  30. 30.Is 92184 divisible by 23?
  31. 31.Is 2869 divisible by 2?
  32. 32.Is 53580 divisible by 8?
  33. 33.Is 2759 divisible by 2?
  34. 34.Is 16579 divisible by 5?
  35. 35.Is 55559 divisible by 8?
  36. 36.Is 58565 divisible by 13?
  37. 37.Is 49400 divisible by 13?
  38. 38.Is 30342 divisible by 5?
  39. 39.Is 5419 divisible by 2?
  40. 40.Is 44890 divisible by 10?

Answer key

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

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