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Divisibility Rules Worksheet

Vedic maths trick 13: Divisibility tests · Set 101 · 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 17287 divisible by 4?
  2. 2.Is 75192 divisible by 12?
  3. 3.Is 52752 divisible by 8?
  4. 4.Is 80330 divisible by 24?
  5. 5.Is 19992 divisible by 6?
  6. 6.Is 60992 divisible by 12?
  7. 7.Is 19160 divisible by 11?
  8. 8.Is 24827 divisible by 11?
  9. 9.Is 9068 divisible by 4?
  10. 10.Is 7286 divisible by 10?
  11. 11.Is 122409 divisible by 29?
  12. 12.Is 6446 divisible by 2?
  13. 13.Is 59320 divisible by 10?
  14. 14.Is 56096 divisible by 24?
  15. 15.Is 202410 divisible by 30?
  16. 16.Is 19685 divisible by 9?
  17. 17.Is 16575 divisible by 15?
  18. 18.Is 199348 divisible by 29?
  19. 19.Is 116722 divisible by 17?
  20. 20.Is 38500 divisible by 20?
  21. 21.Is 105936 divisible by 23?
  22. 22.Is 195060 divisible by 30?
  23. 23.Is 4310 divisible by 2?
  24. 24.Is 72423 divisible by 11?
  25. 25.Is 51540 divisible by 20?
  26. 26.Is 91185 divisible by 15?
  27. 27.Is 71855 divisible by 24?
  28. 28.Is 135460 divisible by 20?
  29. 29.Is 9756 divisible by 3?
  30. 30.Is 19952 divisible by 3?
  31. 31.Is 2660 divisible by 7?
  32. 32.Is 22153 divisible by 12?
  33. 33.Is 50508 divisible by 23?
  34. 34.Is 22885 divisible by 23?
  35. 35.Is 89815 divisible by 23?
  36. 36.Is 33747 divisible by 15?
  37. 37.Is 14948 divisible by 12?
  38. 38.Is 32990 divisible by 5?
  39. 39.Is 55677 divisible by 8?
  40. 40.Is 9627 divisible by 2?

Answer key

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

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