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Divisibility Rules Worksheet

Vedic maths trick 13: Divisibility tests · Set 509 · 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 32656 divisible by 13?
  2. 2.Is 150024 divisible by 24?
  3. 3.Is 189169 divisible by 29?
  4. 4.Is 60261 divisible by 17?
  5. 5.Is 53384 divisible by 8?
  6. 6.Is 16726 divisible by 30?
  7. 7.Is 11286 divisible by 2?
  8. 8.Is 48674 divisible by 8?
  9. 9.Is 11634 divisible by 2?
  10. 10.Is 82844 divisible by 15?
  11. 11.Is 43207 divisible by 8?
  12. 12.Is 3163 divisible by 7?
  13. 13.Is 6819 divisible by 2?
  14. 14.Is 29748 divisible by 15?
  15. 15.Is 39394 divisible by 6?
  16. 16.Is 13897 divisible by 3?
  17. 17.Is 46734 divisible by 29?
  18. 18.Is 6316 divisible by 3?
  19. 19.Is 18324 divisible by 12?
  20. 20.Is 20649 divisible by 6?
  21. 21.Is 35631 divisible by 6?
  22. 22.Is 130267 divisible by 23?
  23. 23.Is 103077 divisible by 30?
  24. 24.Is 1045 divisible by 19?
  25. 25.Is 40122 divisible by 29?
  26. 26.Is 31229 divisible by 20?
  27. 27.Is 197991 divisible by 29?
  28. 28.Is 22475 divisible by 5?
  29. 29.Is 23674 divisible by 4?
  30. 30.Is 11917 divisible by 17?
  31. 31.Is 18454 divisible by 6?
  32. 32.Is 12935 divisible by 5?
  33. 33.Is 9334 divisible by 2?
  34. 34.Is 24453 divisible by 17?
  35. 35.Is 1700 divisible by 2?
  36. 36.Is 9269 divisible by 4?
  37. 37.Is 13752 divisible by 2?
  38. 38.Is 54955 divisible by 10?
  39. 39.Is 92635 divisible by 19?
  40. 40.Is 8443 divisible by 13?

Answer key

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

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