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Divisibility Rules Worksheet

Vedic maths trick 13: Divisibility tests · Set 602 · 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 117646 divisible by 19?
  2. 2.Is 15986 divisible by 6?
  3. 3.Is 106678 divisible by 20?
  4. 4.Is 15715 divisible by 6?
  5. 5.Is 23554 divisible by 5?
  6. 6.Is 64700 divisible by 19?
  7. 7.Is 48583 divisible by 24?
  8. 8.Is 1215 divisible by 23?
  9. 9.Is 68735 divisible by 12?
  10. 10.Is 23094 divisible by 20?
  11. 11.Is 12457 divisible by 29?
  12. 12.Is 36767 divisible by 13?
  13. 13.Is 2439 divisible by 4?
  14. 14.Is 11083 divisible by 3?
  15. 15.Is 8882 divisible by 3?
  16. 16.Is 30042 divisible by 5?
  17. 17.Is 45480 divisible by 10?
  18. 18.Is 37059 divisible by 11?
  19. 19.Is 45118 divisible by 17?
  20. 20.Is 29491 divisible by 10?
  21. 21.Is 4081 divisible by 3?
  22. 22.Is 13797 divisible by 2?
  23. 23.Is 7488 divisible by 4?
  24. 24.Is 32581 divisible by 5?
  25. 25.Is 26052 divisible by 13?
  26. 26.Is 1620 divisible by 10?
  27. 27.Is 83861 divisible by 12?
  28. 28.Is 104158 divisible by 19?
  29. 29.Is 13668 divisible by 11?
  30. 30.Is 40411 divisible by 30?
  31. 31.Is 18673 divisible by 24?
  32. 32.Is 13831 divisible by 4?
  33. 33.Is 6504 divisible by 8?
  34. 34.Is 10344 divisible by 4?
  35. 35.Is 57291 divisible by 13?
  36. 36.Is 41344 divisible by 8?
  37. 37.Is 39848 divisible by 17?
  38. 38.Is 33762 divisible by 15?
  39. 39.Is 21563 divisible by 5?
  40. 40.Is 8134 divisible by 9?

Answer key

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

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