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Divisibility Rules Worksheet

Vedic maths trick 13: Divisibility tests · Set 532 · 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 63140 divisible by 20?
  2. 2.Is 17118 divisible by 3?
  3. 3.Is 123467 divisible by 29?
  4. 4.Is 12783 divisible by 2?
  5. 5.Is 11268 divisible by 9?
  6. 6.Is 131976 divisible by 24?
  7. 7.Is 137394 divisible by 29?
  8. 8.Is 45994 divisible by 29?
  9. 9.Is 2674 divisible by 3?
  10. 10.Is 913 divisible by 2?
  11. 11.Is 4238 divisible by 13?
  12. 12.Is 32773 divisible by 8?
  13. 13.Is 4911 divisible by 3?
  14. 14.Is 86277 divisible by 13?
  15. 15.Is 92322 divisible by 23?
  16. 16.Is 30958 divisible by 5?
  17. 17.Is 58941 divisible by 10?
  18. 18.Is 10412 divisible by 10?
  19. 19.Is 13459 divisible by 2?
  20. 20.Is 164546 divisible by 29?
  21. 21.Is 41590 divisible by 9?
  22. 22.Is 8541 divisible by 13?
  23. 23.Is 73457 divisible by 17?
  24. 24.Is 67610 divisible by 10?
  25. 25.Is 7723 divisible by 2?
  26. 26.Is 76186 divisible by 19?
  27. 27.Is 30974 divisible by 5?
  28. 28.Is 108860 divisible by 24?
  29. 29.Is 68310 divisible by 30?
  30. 30.Is 39536 divisible by 13?
  31. 31.Is 8541 divisible by 2?
  32. 32.Is 3691 divisible by 5?
  33. 33.Is 61728 divisible by 12?
  34. 34.Is 39183 divisible by 7?
  35. 35.Is 104796 divisible by 18?
  36. 36.Is 39033 divisible by 9?
  37. 37.Is 57171 divisible by 17?
  38. 38.Is 110030 divisible by 20?
  39. 39.Is 70065 divisible by 15?
  40. 40.Is 39005 divisible by 29?

Answer key

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

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