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Divisibility Rules Worksheet

Vedic maths trick 13: Divisibility tests · Set 8 · 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 50865 divisible by 15?
  2. 2.Is 109814 divisible by 20?
  3. 3.Is 17549 divisible by 6?
  4. 4.Is 30510 divisible by 5?
  5. 5.Is 26462 divisible by 6?
  6. 6.Is 61716 divisible by 12?
  7. 7.Is 81804 divisible by 12?
  8. 8.Is 120267 divisible by 23?
  9. 9.Is 52584 divisible by 10?
  10. 10.Is 30148 divisible by 8?
  11. 11.Is 26218 divisible by 10?
  12. 12.Is 33281 divisible by 15?
  13. 13.Is 148200 divisible by 30?
  14. 14.Is 5692 divisible by 2?
  15. 15.Is 103965 divisible by 29?
  16. 16.Is 50120 divisible by 8?
  17. 17.Is 4488 divisible by 12?
  18. 18.Is 15540 divisible by 6?
  19. 19.Is 6120 divisible by 8?
  20. 20.Is 38997 divisible by 23?
  21. 21.Is 5622 divisible by 6?
  22. 22.Is 39953 divisible by 11?
  23. 23.Is 5773 divisible by 8?
  24. 24.Is 79380 divisible by 30?
  25. 25.Is 30962 divisible by 8?
  26. 26.Is 49062 divisible by 17?
  27. 27.Is 8312 divisible by 2?
  28. 28.Is 14721 divisible by 3?
  29. 29.Is 10208 divisible by 29?
  30. 30.Is 36496 divisible by 8?
  31. 31.Is 107090 divisible by 17?
  32. 32.Is 29110 divisible by 6?
  33. 33.Is 29640 divisible by 10?
  34. 34.Is 84651 divisible by 29?
  35. 35.Is 9300 divisible by 4?
  36. 36.Is 19365 divisible by 3?
  37. 37.Is 28980 divisible by 23?
  38. 38.Is 27318 divisible by 6?
  39. 39.Is 14069 divisible by 15?
  40. 40.Is 17902 divisible by 3?

Answer key

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

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