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Divisibility Rules Worksheet

Vedic maths trick 13: Divisibility tests · Set 642 · 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 27953 divisible by 11?
  2. 2.Is 57240 divisible by 10?
  3. 3.Is 142918 divisible by 24?
  4. 4.Is 56436 divisible by 19?
  5. 5.Is 38191 divisible by 8?
  6. 6.Is 124170 divisible by 30?
  7. 7.Is 120941 divisible by 20?
  8. 8.Is 54072 divisible by 10?
  9. 9.Is 26406 divisible by 24?
  10. 10.Is 140714 divisible by 29?
  11. 11.Is 27848 divisible by 15?
  12. 12.Is 24073 divisible by 4?
  13. 13.Is 47635 divisible by 11?
  14. 14.Is 103178 divisible by 23?
  15. 15.Is 124642 divisible by 29?
  16. 16.Is 51610 divisible by 17?
  17. 17.Is 9251 divisible by 8?
  18. 18.Is 7062 divisible by 11?
  19. 19.Is 39740 divisible by 13?
  20. 20.Is 20254 divisible by 3?
  21. 21.Is 65086 divisible by 10?
  22. 22.Is 83421 divisible by 19?
  23. 23.Is 29259 divisible by 6?
  24. 24.Is 31493 divisible by 8?
  25. 25.Is 23912 divisible by 8?
  26. 26.Is 40059 divisible by 6?
  27. 27.Is 53414 divisible by 17?
  28. 28.Is 5088 divisible by 4?
  29. 29.Is 32336 divisible by 8?
  30. 30.Is 16024 divisible by 8?
  31. 31.Is 31515 divisible by 7?
  32. 32.Is 37800 divisible by 30?
  33. 33.Is 77961 divisible by 13?
  34. 34.Is 42852 divisible by 18?
  35. 35.Is 73106 divisible by 11?
  36. 36.Is 77599 divisible by 12?
  37. 37.Is 60879 divisible by 13?
  38. 38.Is 25972 divisible by 4?
  39. 39.Is 80811 divisible by 30?
  40. 40.Is 81347 divisible by 17?

Answer key

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

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