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Divisibility Rules Worksheet

Vedic maths trick 13: Divisibility tests · Set 492 · 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 89158 divisible by 13?
  2. 2.Is 9538 divisible by 20?
  3. 3.Is 36651 divisible by 10?
  4. 4.Is 48700 divisible by 10?
  5. 5.Is 37344 divisible by 24?
  6. 6.Is 2599 divisible by 23?
  7. 7.Is 33809 divisible by 6?
  8. 8.Is 39147 divisible by 7?
  9. 9.Is 3630 divisible by 9?
  10. 10.Is 84853 divisible by 15?
  11. 11.Is 4090 divisible by 6?
  12. 12.Is 46728 divisible by 8?
  13. 13.Is 118092 divisible by 17?
  14. 14.Is 18494 divisible by 3?
  15. 15.Is 66890 divisible by 10?
  16. 16.Is 24672 divisible by 24?
  17. 17.Is 104562 divisible by 18?
  18. 18.Is 137220 divisible by 30?
  19. 19.Is 119971 divisible by 20?
  20. 20.Is 39860 divisible by 20?
  21. 21.Is 16505 divisible by 5?
  22. 22.Is 46775 divisible by 30?
  23. 23.Is 1010 divisible by 4?
  24. 24.Is 53176 divisible by 17?
  25. 25.Is 7112 divisible by 4?
  26. 26.Is 8682 divisible by 3?
  27. 27.Is 77109 divisible by 17?
  28. 28.Is 130752 divisible by 24?
  29. 29.Is 13458 divisible by 2?
  30. 30.Is 9359 divisible by 2?
  31. 31.Is 10747 divisible by 7?
  32. 32.Is 8712 divisible by 5?
  33. 33.Is 23676 divisible by 13?
  34. 34.Is 27106 divisible by 10?
  35. 35.Is 80619 divisible by 15?
  36. 36.Is 45425 divisible by 23?
  37. 37.Is 101858 divisible by 23?
  38. 38.Is 12122 divisible by 2?
  39. 39.Is 2077 divisible by 2?
  40. 40.Is 16785 divisible by 13?

Answer key

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

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