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Divisibility Rules Worksheet

Vedic maths trick 13: Divisibility tests · Set 874 · 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 35519 divisible by 7?
  2. 2.Is 152260 divisible by 23?
  3. 3.Is 12519 divisible by 2?
  4. 4.Is 45326 divisible by 11?
  5. 5.Is 89895 divisible by 15?
  6. 6.Is 3220 divisible by 3?
  7. 7.Is 11090 divisible by 2?
  8. 8.Is 53640 divisible by 8?
  9. 9.Is 59040 divisible by 12?
  10. 10.Is 21582 divisible by 4?
  11. 11.Is 10106 divisible by 2?
  12. 12.Is 9189 divisible by 3?
  13. 13.Is 11547 divisible by 9?
  14. 14.Is 88104 divisible by 24?
  15. 15.Is 109931 divisible by 20?
  16. 16.Is 30840 divisible by 8?
  17. 17.Is 30803 divisible by 5?
  18. 18.Is 64536 divisible by 15?
  19. 19.Is 11830 divisible by 3?
  20. 20.Is 77708 divisible by 13?
  21. 21.Is 36309 divisible by 6?
  22. 22.Is 16512 divisible by 5?
  23. 23.Is 86346 divisible by 13?
  24. 24.Is 1414 divisible by 15?
  25. 25.Is 25784 divisible by 4?
  26. 26.Is 42783 divisible by 24?
  27. 27.Is 61380 divisible by 12?
  28. 28.Is 12461 divisible by 8?
  29. 29.Is 1763 divisible by 3?
  30. 30.Is 47355 divisible by 11?
  31. 31.Is 8270 divisible by 5?
  32. 32.Is 92701 divisible by 17?
  33. 33.Is 25956 divisible by 4?
  34. 34.Is 12657 divisible by 2?
  35. 35.Is 61306 divisible by 9?
  36. 36.Is 3471 divisible by 3?
  37. 37.Is 79815 divisible by 17?
  38. 38.Is 109740 divisible by 30?
  39. 39.Is 23700 divisible by 11?
  40. 40.Is 21147 divisible by 19?

Answer key

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

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