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Divisibility Rules Worksheet

Vedic maths trick 13: Divisibility tests · Set 109 · 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 5266 divisible by 4?
  2. 2.Is 47219 divisible by 13?
  3. 3.Is 14053 divisible by 13?
  4. 4.Is 56908 divisible by 29?
  5. 5.Is 128076 divisible by 20?
  6. 6.Is 159979 divisible by 24?
  7. 7.Is 8268 divisible by 2?
  8. 8.Is 88825 divisible by 17?
  9. 9.Is 4785 divisible by 15?
  10. 10.Is 11914 divisible by 24?
  11. 11.Is 32005 divisible by 29?
  12. 12.Is 11007 divisible by 2?
  13. 13.Is 61290 divisible by 18?
  14. 14.Is 155070 divisible by 30?
  15. 15.Is 68870 divisible by 10?
  16. 16.Is 118116 divisible by 17?
  17. 17.Is 108320 divisible by 20?
  18. 18.Is 14360 divisible by 4?
  19. 19.Is 108201 divisible by 24?
  20. 20.Is 13134 divisible by 6?
  21. 21.Is 69309 divisible by 17?
  22. 22.Is 6585 divisible by 5?
  23. 23.Is 16128 divisible by 18?
  24. 24.Is 27568 divisible by 30?
  25. 25.Is 16815 divisible by 5?
  26. 26.Is 10286 divisible by 3?
  27. 27.Is 52875 divisible by 15?
  28. 28.Is 1421 divisible by 11?
  29. 29.Is 9211 divisible by 5?
  30. 30.Is 71272 divisible by 15?
  31. 31.Is 4724 divisible by 23?
  32. 32.Is 2548 divisible by 7?
  33. 33.Is 5797 divisible by 2?
  34. 34.Is 54468 divisible by 18?
  35. 35.Is 42352 divisible by 8?
  36. 36.Is 3913 divisible by 6?
  37. 37.Is 48484 divisible by 9?
  38. 38.Is 18860 divisible by 20?
  39. 39.Is 61951 divisible by 15?
  40. 40.Is 12684 divisible by 7?

Answer key

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

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