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Divisibility Rules Worksheet

Vedic maths trick 13: Divisibility tests · Set 329 · 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 14008 divisible by 15?
  2. 2.Is 7803 divisible by 3?
  3. 3.Is 15080 divisible by 8?
  4. 4.Is 89578 divisible by 17?
  5. 5.Is 87445 divisible by 23?
  6. 6.Is 35316 divisible by 7?
  7. 7.Is 54756 divisible by 11?
  8. 8.Is 38778 divisible by 13?
  9. 9.Is 60969 divisible by 11?
  10. 10.Is 19381 divisible by 3?
  11. 11.Is 17140 divisible by 20?
  12. 12.Is 23282 divisible by 4?
  13. 13.Is 45270 divisible by 9?
  14. 14.Is 11842 divisible by 2?
  15. 15.Is 23960 divisible by 5?
  16. 16.Is 26066 divisible by 4?
  17. 17.Is 28141 divisible by 7?
  18. 18.Is 10913 divisible by 7?
  19. 19.Is 33947 divisible by 12?
  20. 20.Is 147477 divisible by 30?
  21. 21.Is 18168 divisible by 4?
  22. 22.Is 27540 divisible by 17?
  23. 23.Is 102321 divisible by 29?
  24. 24.Is 26020 divisible by 20?
  25. 25.Is 17514 divisible by 3?
  26. 26.Is 7019 divisible by 2?
  27. 27.Is 8185 divisible by 2?
  28. 28.Is 43771 divisible by 17?
  29. 29.Is 22785 divisible by 5?
  30. 30.Is 156343 divisible by 23?
  31. 31.Is 26752 divisible by 8?
  32. 32.Is 49960 divisible by 15?
  33. 33.Is 21475 divisible by 4?
  34. 34.Is 15035 divisible by 10?
  35. 35.Is 36108 divisible by 12?
  36. 36.Is 39777 divisible by 6?
  37. 37.Is 22059 divisible by 11?
  38. 38.Is 166119 divisible by 24?
  39. 39.Is 107352 divisible by 18?
  40. 40.Is 64697 divisible by 11?

Answer key

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

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