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Divisibility Rules Worksheet

Vedic maths trick 13: Divisibility tests · Set 726 · 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 175560 divisible by 30?
  2. 2.Is 20030 divisible by 5?
  3. 3.Is 3663 divisible by 3?
  4. 4.Is 81313 divisible by 17?
  5. 5.Is 3476 divisible by 12?
  6. 6.Is 68320 divisible by 11?
  7. 7.Is 44670 divisible by 8?
  8. 8.Is 88209 divisible by 23?
  9. 9.Is 144768 divisible by 24?
  10. 10.Is 25064 divisible by 8?
  11. 11.Is 2589 divisible by 2?
  12. 12.Is 36130 divisible by 10?
  13. 13.Is 11010 divisible by 6?
  14. 14.Is 12317 divisible by 3?
  15. 15.Is 13579 divisible by 15?
  16. 16.Is 55072 divisible by 8?
  17. 17.Is 12841 divisible by 2?
  18. 18.Is 67180 divisible by 20?
  19. 19.Is 2618 divisible by 17?
  20. 20.Is 49660 divisible by 10?
  21. 21.Is 14651 divisible by 13?
  22. 22.Is 8697 divisible by 13?
  23. 23.Is 4592 divisible by 7?
  24. 24.Is 1438 divisible by 3?
  25. 25.Is 38501 divisible by 11?
  26. 26.Is 37427 divisible by 29?
  27. 27.Is 25671 divisible by 5?
  28. 28.Is 12008 divisible by 2?
  29. 29.Is 132044 divisible by 23?
  30. 30.Is 60094 divisible by 11?
  31. 31.Is 16908 divisible by 10?
  32. 32.Is 31639 divisible by 29?
  33. 33.Is 100546 divisible by 17?
  34. 34.Is 6381 divisible by 5?
  35. 35.Is 158760 divisible by 30?
  36. 36.Is 17890 divisible by 12?
  37. 37.Is 11112 divisible by 24?
  38. 38.Is 20752 divisible by 4?
  39. 39.Is 78885 divisible by 15?
  40. 40.Is 4100 divisible by 20?

Answer key

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

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