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Divisibility Rules Worksheet

Vedic maths trick 13: Divisibility tests · Set 170 · 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 26442 divisible by 13?
  2. 2.Is 38392 divisible by 11?
  3. 3.Is 34212 divisible by 17?
  4. 4.Is 49837 divisible by 19?
  5. 5.Is 61998 divisible by 13?
  6. 6.Is 2030 divisible by 12?
  7. 7.Is 94154 divisible by 18?
  8. 8.Is 40104 divisible by 12?
  9. 9.Is 183031 divisible by 29?
  10. 10.Is 35472 divisible by 23?
  11. 11.Is 104740 divisible by 20?
  12. 12.Is 4350 divisible by 3?
  13. 13.Is 36433 divisible by 6?
  14. 14.Is 12702 divisible by 2?
  15. 15.Is 19724 divisible by 8?
  16. 16.Is 9009 divisible by 11?
  17. 17.Is 4444 divisible by 3?
  18. 18.Is 51388 divisible by 29?
  19. 19.Is 29766 divisible by 11?
  20. 20.Is 49446 divisible by 17?
  21. 21.Is 4415 divisible by 2?
  22. 22.Is 41562 divisible by 7?
  23. 23.Is 169556 divisible by 29?
  24. 24.Is 18089 divisible by 3?
  25. 25.Is 18588 divisible by 4?
  26. 26.Is 19311 divisible by 3?
  27. 27.Is 11580 divisible by 3?
  28. 28.Is 22856 divisible by 7?
  29. 29.Is 57375 divisible by 15?
  30. 30.Is 25771 divisible by 7?
  31. 31.Is 84366 divisible by 18?
  32. 32.Is 15807 divisible by 11?
  33. 33.Is 4370 divisible by 10?
  34. 34.Is 31423 divisible by 7?
  35. 35.Is 10886 divisible by 30?
  36. 36.Is 30811 divisible by 10?
  37. 37.Is 8902 divisible by 18?
  38. 38.Is 16182 divisible by 6?
  39. 39.Is 9384 divisible by 11?
  40. 40.Is 52256 divisible by 12?

Answer key

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

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