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Divisibility Rules Worksheet

Vedic maths trick 13: Divisibility tests · Set 935 · 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 3211 divisible by 19?
  2. 2.Is 13599 divisible by 2?
  3. 3.Is 158529 divisible by 24?
  4. 4.Is 65337 divisible by 10?
  5. 5.Is 161711 divisible by 30?
  6. 6.Is 50042 divisible by 8?
  7. 7.Is 121560 divisible by 30?
  8. 8.Is 6034 divisible by 3?
  9. 9.Is 58497 divisible by 17?
  10. 10.Is 19705 divisible by 5?
  11. 11.Is 50469 divisible by 11?
  12. 12.Is 33520 divisible by 8?
  13. 13.Is 48120 divisible by 7?
  14. 14.Is 2088 divisible by 29?
  15. 15.Is 19184 divisible by 9?
  16. 16.Is 26901 divisible by 15?
  17. 17.Is 6297 divisible by 4?
  18. 18.Is 46547 divisible by 15?
  19. 19.Is 34802 divisible by 7?
  20. 20.Is 18678 divisible by 17?
  21. 21.Is 14300 divisible by 4?
  22. 22.Is 24832 divisible by 8?
  23. 23.Is 12112 divisible by 2?
  24. 24.Is 28453 divisible by 18?
  25. 25.Is 32582 divisible by 11?
  26. 26.Is 90172 divisible by 15?
  27. 27.Is 76800 divisible by 20?
  28. 28.Is 15756 divisible by 9?
  29. 29.Is 62320 divisible by 20?
  30. 30.Is 19150 divisible by 10?
  31. 31.Is 37587 divisible by 17?
  32. 32.Is 1935 divisible by 5?
  33. 33.Is 1197 divisible by 13?
  34. 34.Is 100080 divisible by 24?
  35. 35.Is 5771 divisible by 3?
  36. 36.Is 10420 divisible by 5?
  37. 37.Is 5672 divisible by 8?
  38. 38.Is 29358 divisible by 8?
  39. 39.Is 9782 divisible by 2?
  40. 40.Is 56870 divisible by 19?

Answer key

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

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