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Divisibility Rules Worksheet

Vedic maths trick 13: Divisibility tests · Set 469 · 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 56652 divisible by 17?
  2. 2.Is 11496 divisible by 6?
  3. 3.Is 3056 divisible by 4?
  4. 4.Is 47739 divisible by 9?
  5. 5.Is 166920 divisible by 24?
  6. 6.Is 18164 divisible by 17?
  7. 7.Is 5848 divisible by 4?
  8. 8.Is 3309 divisible by 3?
  9. 9.Is 19796 divisible by 7?
  10. 10.Is 22789 divisible by 15?
  11. 11.Is 6539 divisible by 7?
  12. 12.Is 112811 divisible by 17?
  13. 13.Is 121447 divisible by 20?
  14. 14.Is 18873 divisible by 10?
  15. 15.Is 5465 divisible by 2?
  16. 16.Is 8802 divisible by 18?
  17. 17.Is 33216 divisible by 11?
  18. 18.Is 20622 divisible by 5?
  19. 19.Is 120984 divisible by 18?
  20. 20.Is 141450 divisible by 30?
  21. 21.Is 14450 divisible by 5?
  22. 22.Is 2014 divisible by 6?
  23. 23.Is 15510 divisible by 15?
  24. 24.Is 57782 divisible by 17?
  25. 25.Is 20251 divisible by 11?
  26. 26.Is 1344 divisible by 4?
  27. 27.Is 48945 divisible by 29?
  28. 28.Is 23040 divisible by 7?
  29. 29.Is 38353 divisible by 7?
  30. 30.Is 55573 divisible by 17?
  31. 31.Is 128910 divisible by 30?
  32. 32.Is 31148 divisible by 13?
  33. 33.Is 141243 divisible by 30?
  34. 34.Is 8211 divisible by 3?
  35. 35.Is 569 divisible by 10?
  36. 36.Is 17845 divisible by 5?
  37. 37.Is 12890 divisible by 2?
  38. 38.Is 55992 divisible by 17?
  39. 39.Is 15738 divisible by 6?
  40. 40.Is 29070 divisible by 18?

Answer key

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

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