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Divisibility Rules Worksheet

Vedic maths trick 13: Divisibility tests · Set 578 · 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 92372 divisible by 30?
  2. 2.Is 45694 divisible by 15?
  3. 3.Is 2009 divisible by 4?
  4. 4.Is 77964 divisible by 12?
  5. 5.Is 13700 divisible by 5?
  6. 6.Is 28236 divisible by 5?
  7. 7.Is 9875 divisible by 10?
  8. 8.Is 27934 divisible by 4?
  9. 9.Is 82788 divisible by 12?
  10. 10.Is 22658 divisible by 6?
  11. 11.Is 83439 divisible by 12?
  12. 12.Is 48734 divisible by 24?
  13. 13.Is 4080 divisible by 15?
  14. 14.Is 50610 divisible by 10?
  15. 15.Is 41521 divisible by 23?
  16. 16.Is 22042 divisible by 4?
  17. 17.Is 1478 divisible by 2?
  18. 18.Is 17697 divisible by 3?
  19. 19.Is 200460 divisible by 30?
  20. 20.Is 21155 divisible by 8?
  21. 21.Is 97420 divisible by 20?
  22. 22.Is 48189 divisible by 19?
  23. 23.Is 90504 divisible by 18?
  24. 24.Is 3798 divisible by 3?
  25. 25.Is 15298 divisible by 3?
  26. 26.Is 53433 divisible by 11?
  27. 27.Is 29480 divisible by 5?
  28. 28.Is 70206 divisible by 15?
  29. 29.Is 24992 divisible by 4?
  30. 30.Is 10274 divisible by 2?
  31. 31.Is 11067 divisible by 17?
  32. 32.Is 11420 divisible by 5?
  33. 33.Is 53980 divisible by 30?
  34. 34.Is 4371 divisible by 2?
  35. 35.Is 3104 divisible by 4?
  36. 36.Is 69796 divisible by 10?
  37. 37.Is 7014 divisible by 5?
  38. 38.Is 66975 divisible by 15?
  39. 39.Is 97297 divisible by 24?
  40. 40.Is 22650 divisible by 5?

Answer key

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

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