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Divisibility Rules Worksheet

Vedic maths trick 13: Divisibility tests · Set 328 · 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 1989 divisible by 11?
  2. 2.Is 5478 divisible by 3?
  3. 3.Is 74564 divisible by 13?
  4. 4.Is 83820 divisible by 15?
  5. 5.Is 125161 divisible by 20?
  6. 6.Is 25861 divisible by 9?
  7. 7.Is 46324 divisible by 13?
  8. 8.Is 3940 divisible by 5?
  9. 9.Is 10437 divisible by 18?
  10. 10.Is 9158 divisible by 19?
  11. 11.Is 1341 divisible by 4?
  12. 12.Is 9866 divisible by 2?
  13. 13.Is 129108 divisible by 29?
  14. 14.Is 22652 divisible by 5?
  15. 15.Is 30812 divisible by 5?
  16. 16.Is 104880 divisible by 24?
  17. 17.Is 113137 divisible by 23?
  18. 18.Is 131196 divisible by 29?
  19. 19.Is 90390 divisible by 23?
  20. 20.Is 30749 divisible by 8?
  21. 21.Is 3736 divisible by 8?
  22. 22.Is 36184 divisible by 11?
  23. 23.Is 1818 divisible by 17?
  24. 24.Is 35865 divisible by 9?
  25. 25.Is 209550 divisible by 30?
  26. 26.Is 73834 divisible by 29?
  27. 27.Is 9265 divisible by 2?
  28. 28.Is 134251 divisible by 20?
  29. 29.Is 73740 divisible by 20?
  30. 30.Is 183222 divisible by 29?
  31. 31.Is 49363 divisible by 18?
  32. 32.Is 1192 divisible by 9?
  33. 33.Is 14220 divisible by 4?
  34. 34.Is 9367 divisible by 7?
  35. 35.Is 18241 divisible by 17?
  36. 36.Is 4356 divisible by 12?
  37. 37.Is 74580 divisible by 15?
  38. 38.Is 30124 divisible by 17?
  39. 39.Is 60589 divisible by 10?
  40. 40.Is 9687 divisible by 20?

Answer key

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

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