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Divisibility Rules Worksheet

Vedic maths trick 13: Divisibility tests · Set 331 · 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 72443 divisible by 15?
  2. 2.Is 20341 divisible by 7?
  3. 3.Is 80115 divisible by 15?
  4. 4.Is 66457 divisible by 23?
  5. 5.Is 95131 divisible by 23?
  6. 6.Is 12844 divisible by 3?
  7. 7.Is 110412 divisible by 18?
  8. 8.Is 25933 divisible by 6?
  9. 9.Is 110866 divisible by 30?
  10. 10.Is 9984 divisible by 2?
  11. 11.Is 11376 divisible by 2?
  12. 12.Is 21656 divisible by 4?
  13. 13.Is 24712 divisible by 11?
  14. 14.Is 9774 divisible by 2?
  15. 15.Is 6026 divisible by 2?
  16. 16.Is 149712 divisible by 24?
  17. 17.Is 117 divisible by 7?
  18. 18.Is 13650 divisible by 30?
  19. 19.Is 564 divisible by 8?
  20. 20.Is 13518 divisible by 3?
  21. 21.Is 46941 divisible by 19?
  22. 22.Is 28315 divisible by 13?
  23. 23.Is 24789 divisible by 7?
  24. 24.Is 8813 divisible by 7?
  25. 25.Is 23996 divisible by 6?
  26. 26.Is 3234 divisible by 4?
  27. 27.Is 53913 divisible by 10?
  28. 28.Is 60996 divisible by 13?
  29. 29.Is 140064 divisible by 24?
  30. 30.Is 59460 divisible by 30?
  31. 31.Is 16428 divisible by 3?
  32. 32.Is 100470 divisible by 15?
  33. 33.Is 90882 divisible by 17?
  34. 34.Is 43497 divisible by 9?
  35. 35.Is 1524 divisible by 2?
  36. 36.Is 12313 divisible by 7?
  37. 37.Is 14614 divisible by 3?
  38. 38.Is 61585 divisible by 18?
  39. 39.Is 121284 divisible by 18?
  40. 40.Is 53241 divisible by 10?

Answer key

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

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