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Divisibility Rules Worksheet

Vedic maths trick 13: Divisibility tests · Set 449 · 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 12936 divisible by 6?
  2. 2.Is 26781 divisible by 20?
  3. 3.Is 28920 divisible by 10?
  4. 4.Is 6629 divisible by 19?
  5. 5.Is 28720 divisible by 29?
  6. 6.Is 30464 divisible by 7?
  7. 7.Is 65809 divisible by 12?
  8. 8.Is 16414 divisible by 4?
  9. 9.Is 31093 divisible by 19?
  10. 10.Is 35728 divisible by 29?
  11. 11.Is 10464 divisible by 6?
  12. 12.Is 1999 divisible by 9?
  13. 13.Is 26058 divisible by 6?
  14. 14.Is 21014 divisible by 5?
  15. 15.Is 12239 divisible by 4?
  16. 16.Is 25750 divisible by 10?
  17. 17.Is 12170 divisible by 2?
  18. 18.Is 10382 divisible by 6?
  19. 19.Is 46116 divisible by 7?
  20. 20.Is 123560 divisible by 20?
  21. 21.Is 103329 divisible by 17?
  22. 22.Is 6059 divisible by 7?
  23. 23.Is 14877 divisible by 4?
  24. 24.Is 4814 divisible by 29?
  25. 25.Is 78225 divisible by 13?
  26. 26.Is 42873 divisible by 7?
  27. 27.Is 12324 divisible by 4?
  28. 28.Is 45083 divisible by 20?
  29. 29.Is 23695 divisible by 20?
  30. 30.Is 21135 divisible by 15?
  31. 31.Is 39573 divisible by 9?
  32. 32.Is 4007 divisible by 5?
  33. 33.Is 16530 divisible by 15?
  34. 34.Is 23800 divisible by 10?
  35. 35.Is 1952 divisible by 6?
  36. 36.Is 51393 divisible by 29?
  37. 37.Is 34512 divisible by 24?
  38. 38.Is 1153 divisible by 7?
  39. 39.Is 12922 divisible by 8?
  40. 40.Is 37071 divisible by 7?

Answer key

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

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