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Divisibility Rules Worksheet

Vedic maths trick 13: Divisibility tests · Set 392 · 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 5542 divisible by 3?
  2. 2.Is 37383 divisible by 6?
  3. 3.Is 162 divisible by 6?
  4. 4.Is 60615 divisible by 15?
  5. 5.Is 83253 divisible by 18?
  6. 6.Is 64104 divisible by 12?
  7. 7.Is 59782 divisible by 18?
  8. 8.Is 15515 divisible by 15?
  9. 9.Is 1700 divisible by 5?
  10. 10.Is 11674 divisible by 13?
  11. 11.Is 43032 divisible by 7?
  12. 12.Is 6413 divisible by 12?
  13. 13.Is 25701 divisible by 8?
  14. 14.Is 3265 divisible by 2?
  15. 15.Is 67787 divisible by 15?
  16. 16.Is 11634 divisible by 2?
  17. 17.Is 55680 divisible by 12?
  18. 18.Is 19181 divisible by 3?
  19. 19.Is 39180 divisible by 12?
  20. 20.Is 65802 divisible by 18?
  21. 21.Is 3194 divisible by 2?
  22. 22.Is 81119 divisible by 12?
  23. 23.Is 83052 divisible by 18?
  24. 24.Is 123970 divisible by 20?
  25. 25.Is 29057 divisible by 9?
  26. 26.Is 3165 divisible by 11?
  27. 27.Is 117453 divisible by 17?
  28. 28.Is 2237 divisible by 18?
  29. 29.Is 74555 divisible by 13?
  30. 30.Is 14777 divisible by 7?
  31. 31.Is 14175 divisible by 7?
  32. 32.Is 20856 divisible by 3?
  33. 33.Is 69642 divisible by 10?
  34. 34.Is 346 divisible by 7?
  35. 35.Is 36047 divisible by 11?
  36. 36.Is 17978 divisible by 19?
  37. 37.Is 23460 divisible by 19?
  38. 38.Is 75888 divisible by 12?
  39. 39.Is 67660 divisible by 17?
  40. 40.Is 119950 divisible by 23?

Answer key

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

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