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Divisibility Rules Worksheet

Vedic maths trick 13: Divisibility tests · Set 70 · 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 123830 divisible by 29?
  2. 2.Is 95040 divisible by 15?
  3. 3.Is 7080 divisible by 24?
  4. 4.Is 6989 divisible by 15?
  5. 5.Is 81269 divisible by 18?
  6. 6.Is 16740 divisible by 4?
  7. 7.Is 13756 divisible by 3?
  8. 8.Is 53337 divisible by 18?
  9. 9.Is 11748 divisible by 4?
  10. 10.Is 80299 divisible by 13?
  11. 11.Is 20941 divisible by 17?
  12. 12.Is 20375 divisible by 5?
  13. 13.Is 8145 divisible by 5?
  14. 14.Is 10240 divisible by 10?
  15. 15.Is 7396 divisible by 2?
  16. 16.Is 2019 divisible by 2?
  17. 17.Is 10198 divisible by 9?
  18. 18.Is 3528 divisible by 6?
  19. 19.Is 21694 divisible by 8?
  20. 20.Is 352 divisible by 19?
  21. 21.Is 27140 divisible by 20?
  22. 22.Is 2189 divisible by 4?
  23. 23.Is 18346 divisible by 23?
  24. 24.Is 20340 divisible by 4?
  25. 25.Is 13604 divisible by 7?
  26. 26.Is 149060 divisible by 29?
  27. 27.Is 15130 divisible by 17?
  28. 28.Is 50618 divisible by 8?
  29. 29.Is 34885 divisible by 11?
  30. 30.Is 2226 divisible by 9?
  31. 31.Is 6079 divisible by 2?
  32. 32.Is 5949 divisible by 10?
  33. 33.Is 53562 divisible by 10?
  34. 34.Is 76488 divisible by 24?
  35. 35.Is 85644 divisible by 13?
  36. 36.Is 33492 divisible by 6?
  37. 37.Is 77457 divisible by 15?
  38. 38.Is 160839 divisible by 23?
  39. 39.Is 59174 divisible by 10?
  40. 40.Is 14854 divisible by 4?

Answer key

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

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