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Divisibility Rules Worksheet

Vedic maths trick 13: Divisibility tests · Set 855 · 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 8531 divisible by 19?
  2. 2.Is 15872 divisible by 4?
  3. 3.Is 37466 divisible by 13?
  4. 4.Is 19788 divisible by 4?
  5. 5.Is 13048 divisible by 8?
  6. 6.Is 18501 divisible by 13?
  7. 7.Is 6597 divisible by 9?
  8. 8.Is 24003 divisible by 30?
  9. 9.Is 80560 divisible by 19?
  10. 10.Is 2247 divisible by 7?
  11. 11.Is 20899 divisible by 11?
  12. 12.Is 21559 divisible by 12?
  13. 13.Is 16337 divisible by 18?
  14. 14.Is 50420 divisible by 20?
  15. 15.Is 73340 divisible by 20?
  16. 16.Is 23310 divisible by 6?
  17. 17.Is 35815 divisible by 13?
  18. 18.Is 21179 divisible by 10?
  19. 19.Is 122236 divisible by 19?
  20. 20.Is 26026 divisible by 11?
  21. 21.Is 11076 divisible by 13?
  22. 22.Is 12476 divisible by 2?
  23. 23.Is 2093 divisible by 10?
  24. 24.Is 6986 divisible by 3?
  25. 25.Is 65930 divisible by 19?
  26. 26.Is 8898 divisible by 2?
  27. 27.Is 32543 divisible by 7?
  28. 28.Is 3216 divisible by 3?
  29. 29.Is 72326 divisible by 29?
  30. 30.Is 85143 divisible by 24?
  31. 31.Is 157740 divisible by 30?
  32. 32.Is 8943 divisible by 3?
  33. 33.Is 39585 divisible by 15?
  34. 34.Is 4916 divisible by 3?
  35. 35.Is 12278 divisible by 17?
  36. 36.Is 41101 divisible by 7?
  37. 37.Is 54059 divisible by 17?
  38. 38.Is 36953 divisible by 7?
  39. 39.Is 6386 divisible by 8?
  40. 40.Is 60671 divisible by 13?

Answer key

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

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