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Divisibility Rules Worksheet

Vedic maths trick 13: Divisibility tests · Set 468 · 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 34548 divisible by 12?
  2. 2.Is 8883 divisible by 9?
  3. 3.Is 21225 divisible by 15?
  4. 4.Is 4151 divisible by 12?
  5. 5.Is 6894 divisible by 4?
  6. 6.Is 32180 divisible by 6?
  7. 7.Is 67040 divisible by 20?
  8. 8.Is 22946 divisible by 8?
  9. 9.Is 11445 divisible by 18?
  10. 10.Is 163712 divisible by 29?
  11. 11.Is 129845 divisible by 20?
  12. 12.Is 16750 divisible by 29?
  13. 13.Is 9240 divisible by 4?
  14. 14.Is 1129 divisible by 7?
  15. 15.Is 2884 divisible by 4?
  16. 16.Is 34309 divisible by 18?
  17. 17.Is 4440 divisible by 5?
  18. 18.Is 37429 divisible by 7?
  19. 19.Is 1750 divisible by 3?
  20. 20.Is 16425 divisible by 4?
  21. 21.Is 35512 divisible by 8?
  22. 22.Is 27958 divisible by 17?
  23. 23.Is 883 divisible by 3?
  24. 24.Is 2688 divisible by 24?
  25. 25.Is 46133 divisible by 13?
  26. 26.Is 20742 divisible by 7?
  27. 27.Is 3521 divisible by 4?
  28. 28.Is 63048 divisible by 18?
  29. 29.Is 15191 divisible by 3?
  30. 30.Is 42388 divisible by 9?
  31. 31.Is 40425 divisible by 7?
  32. 32.Is 67236 divisible by 30?
  33. 33.Is 12587 divisible by 2?
  34. 34.Is 30573 divisible by 11?
  35. 35.Is 3066 divisible by 13?
  36. 36.Is 2267 divisible by 2?
  37. 37.Is 31586 divisible by 17?
  38. 38.Is 102915 divisible by 15?
  39. 39.Is 6573 divisible by 2?
  40. 40.Is 17043 divisible by 19?

Answer key

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

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