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Divisibility Rules Worksheet

Vedic maths trick 13: Divisibility tests · Set 727 · 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 19588 divisible by 4?
  2. 2.Is 10753 divisible by 17?
  3. 3.Is 8850 divisible by 3?
  4. 4.Is 96687 divisible by 23?
  5. 5.Is 26581 divisible by 11?
  6. 6.Is 2335 divisible by 7?
  7. 7.Is 68356 divisible by 12?
  8. 8.Is 2127 divisible by 2?
  9. 9.Is 75876 divisible by 11?
  10. 10.Is 11298 divisible by 6?
  11. 11.Is 2612 divisible by 3?
  12. 12.Is 57271 divisible by 13?
  13. 13.Is 4626 divisible by 18?
  14. 14.Is 42695 divisible by 7?
  15. 15.Is 71880 divisible by 24?
  16. 16.Is 49648 divisible by 29?
  17. 17.Is 67608 divisible by 24?
  18. 18.Is 72712 divisible by 11?
  19. 19.Is 24365 divisible by 11?
  20. 20.Is 4654 divisible by 19?
  21. 21.Is 2274 divisible by 2?
  22. 22.Is 3114 divisible by 5?
  23. 23.Is 38345 divisible by 17?
  24. 24.Is 45608 divisible by 8?
  25. 25.Is 22939 divisible by 29?
  26. 26.Is 1687 divisible by 3?
  27. 27.Is 49844 divisible by 17?
  28. 28.Is 29367 divisible by 23?
  29. 29.Is 74291 divisible by 18?
  30. 30.Is 108405 divisible by 20?
  31. 31.Is 35658 divisible by 7?
  32. 32.Is 10427 divisible by 12?
  33. 33.Is 52929 divisible by 29?
  34. 34.Is 72619 divisible by 12?
  35. 35.Is 23870 divisible by 7?
  36. 36.Is 7756 divisible by 2?
  37. 37.Is 2020 divisible by 20?
  38. 38.Is 37515 divisible by 11?
  39. 39.Is 76194 divisible by 18?
  40. 40.Is 2975 divisible by 17?

Answer key

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

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