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Divisibility Rules Worksheet

Vedic maths trick 13: Divisibility tests · Set 564 · 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 75309 divisible by 23?
  2. 2.Is 24092 divisible by 8?
  3. 3.Is 110242 divisible by 30?
  4. 4.Is 33642 divisible by 10?
  5. 5.Is 17544 divisible by 17?
  6. 6.Is 1363 divisible by 2?
  7. 7.Is 5775 divisible by 3?
  8. 8.Is 18960 divisible by 7?
  9. 9.Is 10266 divisible by 4?
  10. 10.Is 73207 divisible by 19?
  11. 11.Is 9684 divisible by 29?
  12. 12.Is 8006 divisible by 29?
  13. 13.Is 8044 divisible by 4?
  14. 14.Is 11144 divisible by 2?
  15. 15.Is 14822 divisible by 17?
  16. 16.Is 5451 divisible by 23?
  17. 17.Is 25524 divisible by 9?
  18. 18.Is 81532 divisible by 30?
  19. 19.Is 104834 divisible by 23?
  20. 20.Is 20318 divisible by 5?
  21. 21.Is 14410 divisible by 10?
  22. 22.Is 64385 divisible by 10?
  23. 23.Is 27430 divisible by 13?
  24. 24.Is 25960 divisible by 4?
  25. 25.Is 23175 divisible by 5?
  26. 26.Is 1976 divisible by 2?
  27. 27.Is 28020 divisible by 12?
  28. 28.Is 29831 divisible by 30?
  29. 29.Is 12992 divisible by 4?
  30. 30.Is 8282 divisible by 4?
  31. 31.Is 51898 divisible by 17?
  32. 32.Is 25795 divisible by 7?
  33. 33.Is 21593 divisible by 23?
  34. 34.Is 64392 divisible by 12?
  35. 35.Is 7738 divisible by 10?
  36. 36.Is 14995 divisible by 9?
  37. 37.Is 28861 divisible by 19?
  38. 38.Is 4149 divisible by 9?
  39. 39.Is 22289 divisible by 29?
  40. 40.Is 41580 divisible by 30?

Answer key

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

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