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Divisibility Rules Worksheet

Vedic maths trick 13: Divisibility tests · Set 675 · 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 22740 divisible by 20?
  2. 2.Is 92112 divisible by 19?
  3. 3.Is 68078 divisible by 12?
  4. 4.Is 38138 divisible by 8?
  5. 5.Is 16781 divisible by 7?
  6. 6.Is 65455 divisible by 19?
  7. 7.Is 36544 divisible by 8?
  8. 8.Is 6291 divisible by 6?
  9. 9.Is 112902 divisible by 24?
  10. 10.Is 21129 divisible by 4?
  11. 11.Is 70182 divisible by 18?
  12. 12.Is 42272 divisible by 9?
  13. 13.Is 42696 divisible by 9?
  14. 14.Is 142968 divisible by 23?
  15. 15.Is 36168 divisible by 24?
  16. 16.Is 27512 divisible by 8?
  17. 17.Is 10705 divisible by 2?
  18. 18.Is 37794 divisible by 6?
  19. 19.Is 1941 divisible by 10?
  20. 20.Is 6149 divisible by 11?
  21. 21.Is 5025 divisible by 3?
  22. 22.Is 1002 divisible by 6?
  23. 23.Is 12170 divisible by 5?
  24. 24.Is 75339 divisible by 11?
  25. 25.Is 6675 divisible by 8?
  26. 26.Is 101196 divisible by 18?
  27. 27.Is 187444 divisible by 30?
  28. 28.Is 11773 divisible by 5?
  29. 29.Is 38367 divisible by 7?
  30. 30.Is 93381 divisible by 17?
  31. 31.Is 82663 divisible by 29?
  32. 32.Is 3302 divisible by 13?
  33. 33.Is 23851 divisible by 23?
  34. 34.Is 37251 divisible by 12?
  35. 35.Is 19388 divisible by 8?
  36. 36.Is 43678 divisible by 15?
  37. 37.Is 113760 divisible by 18?
  38. 38.Is 117660 divisible by 30?
  39. 39.Is 13972 divisible by 7?
  40. 40.Is 8380 divisible by 18?

Answer key

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

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