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Divisibility Rules Worksheet

Vedic maths trick 13: Divisibility tests · Set 487 · 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 4849 divisible by 13?
  2. 2.Is 78775 divisible by 23?
  3. 3.Is 78871 divisible by 13?
  4. 4.Is 14280 divisible by 3?
  5. 5.Is 43044 divisible by 12?
  6. 6.Is 105791 divisible by 17?
  7. 7.Is 16860 divisible by 10?
  8. 8.Is 63330 divisible by 15?
  9. 9.Is 156690 divisible by 30?
  10. 10.Is 34032 divisible by 6?
  11. 11.Is 10308 divisible by 6?
  12. 12.Is 61856 divisible by 11?
  13. 13.Is 13336 divisible by 9?
  14. 14.Is 44965 divisible by 18?
  15. 15.Is 30183 divisible by 29?
  16. 16.Is 17573 divisible by 9?
  17. 17.Is 7139 divisible by 3?
  18. 18.Is 49935 divisible by 15?
  19. 19.Is 20531 divisible by 3?
  20. 20.Is 17560 divisible by 4?
  21. 21.Is 83700 divisible by 30?
  22. 22.Is 7061 divisible by 23?
  23. 23.Is 16795 divisible by 3?
  24. 24.Is 14824 divisible by 4?
  25. 25.Is 15734 divisible by 3?
  26. 26.Is 58554 divisible by 9?
  27. 27.Is 42162 divisible by 9?
  28. 28.Is 47786 divisible by 8?
  29. 29.Is 35160 divisible by 6?
  30. 30.Is 3332 divisible by 7?
  31. 31.Is 4693 divisible by 19?
  32. 32.Is 37091 divisible by 11?
  33. 33.Is 27153 divisible by 19?
  34. 34.Is 29166 divisible by 8?
  35. 35.Is 10892 divisible by 4?
  36. 36.Is 10295 divisible by 5?
  37. 37.Is 27552 divisible by 7?
  38. 38.Is 64172 divisible by 17?
  39. 39.Is 42957 divisible by 9?
  40. 40.Is 3021 divisible by 13?

Answer key

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

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