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Divisibility Rules Worksheet

Vedic maths trick 13: Divisibility tests · Set 919 · 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 2431 divisible by 17?
  2. 2.Is 9266 divisible by 9?
  3. 3.Is 26610 divisible by 4?
  4. 4.Is 28207 divisible by 18?
  5. 5.Is 46529 divisible by 17?
  6. 6.Is 32533 divisible by 8?
  7. 7.Is 22526 divisible by 7?
  8. 8.Is 32555 divisible by 19?
  9. 9.Is 2408 divisible by 4?
  10. 10.Is 2070 divisible by 18?
  11. 11.Is 9855 divisible by 8?
  12. 12.Is 35354 divisible by 11?
  13. 13.Is 2129 divisible by 2?
  14. 14.Is 6284 divisible by 3?
  15. 15.Is 14659 divisible by 3?
  16. 16.Is 10698 divisible by 6?
  17. 17.Is 6293 divisible by 29?
  18. 18.Is 91720 divisible by 20?
  19. 19.Is 25900 divisible by 10?
  20. 20.Is 12648 divisible by 24?
  21. 21.Is 56728 divisible by 9?
  22. 22.Is 7929 divisible by 2?
  23. 23.Is 81649 divisible by 24?
  24. 24.Is 69760 divisible by 29?
  25. 25.Is 14897 divisible by 7?
  26. 26.Is 53721 divisible by 9?
  27. 27.Is 122323 divisible by 30?
  28. 28.Is 102249 divisible by 15?
  29. 29.Is 37243 divisible by 23?
  30. 30.Is 130967 divisible by 19?
  31. 31.Is 5999 divisible by 6?
  32. 32.Is 41046 divisible by 6?
  33. 33.Is 57460 divisible by 10?
  34. 34.Is 29412 divisible by 19?
  35. 35.Is 32005 divisible by 19?
  36. 36.Is 75661 divisible by 23?
  37. 37.Is 161385 divisible by 29?
  38. 38.Is 106372 divisible by 18?
  39. 39.Is 64722 divisible by 23?
  40. 40.Is 4578 divisible by 6?

Answer key

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

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