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Divisibility Rules Worksheet

Vedic maths trick 13: Divisibility tests · Set 21 · 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 95255 divisible by 20?
  2. 2.Is 41921 divisible by 11?
  3. 3.Is 64236 divisible by 12?
  4. 4.Is 26125 divisible by 11?
  5. 5.Is 92955 divisible by 15?
  6. 6.Is 126520 divisible by 20?
  7. 7.Is 22851 divisible by 10?
  8. 8.Is 13865 divisible by 2?
  9. 9.Is 13899 divisible by 3?
  10. 10.Is 415 divisible by 4?
  11. 11.Is 73399 divisible by 12?
  12. 12.Is 84559 divisible by 19?
  13. 13.Is 9796 divisible by 23?
  14. 14.Is 21710 divisible by 13?
  15. 15.Is 22641 divisible by 18?
  16. 16.Is 117667 divisible by 19?
  17. 17.Is 919 divisible by 6?
  18. 18.Is 35739 divisible by 13?
  19. 19.Is 22907 divisible by 7?
  20. 20.Is 69629 divisible by 29?
  21. 21.Is 39780 divisible by 18?
  22. 22.Is 19734 divisible by 3?
  23. 23.Is 189921 divisible by 29?
  24. 24.Is 67035 divisible by 20?
  25. 25.Is 44029 divisible by 8?
  26. 26.Is 17280 divisible by 24?
  27. 27.Is 19693 divisible by 4?
  28. 28.Is 159919 divisible by 23?
  29. 29.Is 103638 divisible by 23?
  30. 30.Is 11262 divisible by 6?
  31. 31.Is 53832 divisible by 11?
  32. 32.Is 28008 divisible by 6?
  33. 33.Is 6553 divisible by 3?
  34. 34.Is 105089 divisible by 18?
  35. 35.Is 82212 divisible by 12?
  36. 36.Is 75334 divisible by 30?
  37. 37.Is 9918 divisible by 6?
  38. 38.Is 18870 divisible by 4?
  39. 39.Is 43400 divisible by 8?
  40. 40.Is 123708 divisible by 30?

Answer key

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

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