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Divisibility Rules Worksheet

Vedic maths trick 13: Divisibility tests · Set 631 · 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 40737 divisible by 7?
  2. 2.Is 13924 divisible by 4?
  3. 3.Is 67309 divisible by 11?
  4. 4.Is 29832 divisible by 24?
  5. 5.Is 69485 divisible by 13?
  6. 6.Is 45482 divisible by 13?
  7. 7.Is 57586 divisible by 10?
  8. 8.Is 12514 divisible by 3?
  9. 9.Is 85150 divisible by 13?
  10. 10.Is 19391 divisible by 8?
  11. 11.Is 36288 divisible by 7?
  12. 12.Is 36007 divisible by 7?
  13. 13.Is 25295 divisible by 5?
  14. 14.Is 3428 divisible by 23?
  15. 15.Is 109292 divisible by 24?
  16. 16.Is 33107 divisible by 11?
  17. 17.Is 6918 divisible by 5?
  18. 18.Is 32613 divisible by 7?
  19. 19.Is 142823 divisible by 23?
  20. 20.Is 26622 divisible by 9?
  21. 21.Is 44848 divisible by 13?
  22. 22.Is 32364 divisible by 12?
  23. 23.Is 64154 divisible by 10?
  24. 24.Is 61188 divisible by 24?
  25. 25.Is 96974 divisible by 15?
  26. 26.Is 9086 divisible by 7?
  27. 27.Is 2547 divisible by 9?
  28. 28.Is 41523 divisible by 12?
  29. 29.Is 176611 divisible by 30?
  30. 30.Is 5633 divisible by 2?
  31. 31.Is 18762 divisible by 3?
  32. 32.Is 17352 divisible by 18?
  33. 33.Is 14549 divisible by 4?
  34. 34.Is 206544 divisible by 30?
  35. 35.Is 8578 divisible by 12?
  36. 36.Is 101434 divisible by 20?
  37. 37.Is 23097 divisible by 29?
  38. 38.Is 32492 divisible by 30?
  39. 39.Is 8182 divisible by 3?
  40. 40.Is 116413 divisible by 19?

Answer key

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

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