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Divisibility Rules Worksheet

Vedic maths trick 13: Divisibility tests · Set 205 · 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 13588 divisible by 9?
  2. 2.Is 71820 divisible by 18?
  3. 3.Is 15870 divisible by 15?
  4. 4.Is 33675 divisible by 15?
  5. 5.Is 44869 divisible by 11?
  6. 6.Is 45260 divisible by 20?
  7. 7.Is 13760 divisible by 10?
  8. 8.Is 33704 divisible by 23?
  9. 9.Is 20307 divisible by 19?
  10. 10.Is 122222 divisible by 23?
  11. 11.Is 6494 divisible by 7?
  12. 12.Is 8325 divisible by 4?
  13. 13.Is 86025 divisible by 15?
  14. 14.Is 129420 divisible by 30?
  15. 15.Is 2910 divisible by 2?
  16. 16.Is 9575 divisible by 17?
  17. 17.Is 19060 divisible by 6?
  18. 18.Is 48546 divisible by 18?
  19. 19.Is 129150 divisible by 30?
  20. 20.Is 42264 divisible by 18?
  21. 21.Is 1632 divisible by 2?
  22. 22.Is 24636 divisible by 6?
  23. 23.Is 110453 divisible by 19?
  24. 24.Is 114318 divisible by 29?
  25. 25.Is 7507 divisible by 3?
  26. 26.Is 2597 divisible by 17?
  27. 27.Is 12505 divisible by 3?
  28. 28.Is 1240 divisible by 10?
  29. 29.Is 4629 divisible by 4?
  30. 30.Is 31785 divisible by 8?
  31. 31.Is 30581 divisible by 23?
  32. 32.Is 198731 divisible by 30?
  33. 33.Is 18745 divisible by 5?
  34. 34.Is 11119 divisible by 11?
  35. 35.Is 4581 divisible by 7?
  36. 36.Is 36243 divisible by 7?
  37. 37.Is 28571 divisible by 6?
  38. 38.Is 93870 divisible by 30?
  39. 39.Is 12910 divisible by 2?
  40. 40.Is 34937 divisible by 6?

Answer key

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

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