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Divisibility Rules Worksheet

Vedic maths trick 13: Divisibility tests · Set 822 · 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 17387 divisible by 13?
  2. 2.Is 34340 divisible by 9?
  3. 3.Is 121793 divisible by 19?
  4. 4.Is 42334 divisible by 24?
  5. 5.Is 9105 divisible by 6?
  6. 6.Is 123571 divisible by 24?
  7. 7.Is 3883 divisible by 9?
  8. 8.Is 80426 divisible by 29?
  9. 9.Is 5800 divisible by 3?
  10. 10.Is 57161 divisible by 13?
  11. 11.Is 20460 divisible by 5?
  12. 12.Is 80940 divisible by 30?
  13. 13.Is 8393 divisible by 7?
  14. 14.Is 297 divisible by 3?
  15. 15.Is 12956 divisible by 7?
  16. 16.Is 4874 divisible by 2?
  17. 17.Is 119299 divisible by 20?
  18. 18.Is 48467 divisible by 13?
  19. 19.Is 12035 divisible by 29?
  20. 20.Is 42744 divisible by 23?
  21. 21.Is 41400 divisible by 10?
  22. 22.Is 1490 divisible by 12?
  23. 23.Is 2574 divisible by 8?
  24. 24.Is 106610 divisible by 20?
  25. 25.Is 31350 divisible by 6?
  26. 26.Is 12966 divisible by 6?
  27. 27.Is 28944 divisible by 24?
  28. 28.Is 39418 divisible by 13?
  29. 29.Is 3370 divisible by 17?
  30. 30.Is 78901 divisible by 13?
  31. 31.Is 47766 divisible by 30?
  32. 32.Is 62199 divisible by 9?
  33. 33.Is 351 divisible by 10?
  34. 34.Is 10149 divisible by 24?
  35. 35.Is 7364 divisible by 3?
  36. 36.Is 55308 divisible by 11?
  37. 37.Is 17077 divisible by 15?
  38. 38.Is 24000 divisible by 6?
  39. 39.Is 24450 divisible by 8?
  40. 40.Is 94031 divisible by 24?

Answer key

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

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