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Divisibility Rules Worksheet

Vedic maths trick 13: Divisibility tests · Set 6 · 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 48460 divisible by 15?
  2. 2.Is 39663 divisible by 12?
  3. 3.Is 26920 divisible by 10?
  4. 4.Is 21266 divisible by 7?
  5. 5.Is 36423 divisible by 6?
  6. 6.Is 47557 divisible by 23?
  7. 7.Is 124110 divisible by 30?
  8. 8.Is 1120 divisible by 2?
  9. 9.Is 79922 divisible by 12?
  10. 10.Is 14358 divisible by 5?
  11. 11.Is 17675 divisible by 3?
  12. 12.Is 10840 divisible by 3?
  13. 13.Is 105378 divisible by 30?
  14. 14.Is 186750 divisible by 30?
  15. 15.Is 27289 divisible by 17?
  16. 16.Is 54461 divisible by 9?
  17. 17.Is 6432 divisible by 3?
  18. 18.Is 73530 divisible by 19?
  19. 19.Is 14438 divisible by 11?
  20. 20.Is 21069 divisible by 4?
  21. 21.Is 1593 divisible by 2?
  22. 22.Is 19207 divisible by 11?
  23. 23.Is 19929 divisible by 11?
  24. 24.Is 12292 divisible by 11?
  25. 25.Is 3706 divisible by 3?
  26. 26.Is 57536 divisible by 9?
  27. 27.Is 47070 divisible by 23?
  28. 28.Is 12108 divisible by 4?
  29. 29.Is 53304 divisible by 12?
  30. 30.Is 17073 divisible by 3?
  31. 31.Is 17765 divisible by 5?
  32. 32.Is 111125 divisible by 20?
  33. 33.Is 48992 divisible by 10?
  34. 34.Is 57434 divisible by 13?
  35. 35.Is 82384 divisible by 19?
  36. 36.Is 69281 divisible by 29?
  37. 37.Is 35507 divisible by 7?
  38. 38.Is 14612 divisible by 23?
  39. 39.Is 11685 divisible by 2?
  40. 40.Is 72712 divisible by 13?

Answer key

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

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