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Divisibility Rules Worksheet

Vedic maths trick 13: Divisibility tests · Set 511 · 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 34200 divisible by 9?
  2. 2.Is 52388 divisible by 30?
  3. 3.Is 89984 divisible by 17?
  4. 4.Is 168360 divisible by 30?
  5. 5.Is 756 divisible by 4?
  6. 6.Is 14712 divisible by 4?
  7. 7.Is 16607 divisible by 7?
  8. 8.Is 163386 divisible by 29?
  9. 9.Is 86783 divisible by 30?
  10. 10.Is 82245 divisible by 29?
  11. 11.Is 55474 divisible by 17?
  12. 12.Is 21210 divisible by 30?
  13. 13.Is 7081 divisible by 7?
  14. 14.Is 74325 divisible by 15?
  15. 15.Is 48042 divisible by 9?
  16. 16.Is 36600 divisible by 20?
  17. 17.Is 13255 divisible by 5?
  18. 18.Is 2040 divisible by 12?
  19. 19.Is 89394 divisible by 24?
  20. 20.Is 19193 divisible by 4?
  21. 21.Is 37879 divisible by 9?
  22. 22.Is 1955 divisible by 15?
  23. 23.Is 17507 divisible by 7?
  24. 24.Is 10882 divisible by 7?
  25. 25.Is 107292 divisible by 20?
  26. 26.Is 70823 divisible by 23?
  27. 27.Is 24835 divisible by 19?
  28. 28.Is 1398 divisible by 3?
  29. 29.Is 37561 divisible by 23?
  30. 30.Is 2355 divisible by 13?
  31. 31.Is 13914 divisible by 18?
  32. 32.Is 48900 divisible by 15?
  33. 33.Is 41976 divisible by 18?
  34. 34.Is 4250 divisible by 4?
  35. 35.Is 135490 divisible by 20?
  36. 36.Is 13142 divisible by 5?
  37. 37.Is 82440 divisible by 18?
  38. 38.Is 27403 divisible by 10?
  39. 39.Is 245 divisible by 10?
  40. 40.Is 74604 divisible by 12?

Answer key

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

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