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Divisibility Rules Worksheet

Vedic maths trick 13: Divisibility tests · Set 704 · 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 5177 divisible by 4?
  2. 2.Is 3811 divisible by 3?
  3. 3.Is 22797 divisible by 5?
  4. 4.Is 1863 divisible by 2?
  5. 5.Is 7623 divisible by 3?
  6. 6.Is 129615 divisible by 24?
  7. 7.Is 20125 divisible by 3?
  8. 8.Is 101482 divisible by 15?
  9. 9.Is 45964 divisible by 13?
  10. 10.Is 10923 divisible by 2?
  11. 11.Is 43128 divisible by 8?
  12. 12.Is 134184 divisible by 24?
  13. 13.Is 29743 divisible by 29?
  14. 14.Is 83520 divisible by 29?
  15. 15.Is 23176 divisible by 8?
  16. 16.Is 52407 divisible by 8?
  17. 17.Is 51444 divisible by 20?
  18. 18.Is 51179 divisible by 9?
  19. 19.Is 29760 divisible by 13?
  20. 20.Is 125172 divisible by 18?
  21. 21.Is 49256 divisible by 8?
  22. 22.Is 11778 divisible by 13?
  23. 23.Is 148440 divisible by 30?
  24. 24.Is 27748 divisible by 7?
  25. 25.Is 52217 divisible by 13?
  26. 26.Is 6580 divisible by 3?
  27. 27.Is 42717 divisible by 29?
  28. 28.Is 31197 divisible by 24?
  29. 29.Is 7583 divisible by 4?
  30. 30.Is 2275 divisible by 13?
  31. 31.Is 12673 divisible by 11?
  32. 32.Is 33597 divisible by 6?
  33. 33.Is 178627 divisible by 29?
  34. 34.Is 2185 divisible by 5?
  35. 35.Is 7853 divisible by 4?
  36. 36.Is 122483 divisible by 19?
  37. 37.Is 46980 divisible by 10?
  38. 38.Is 127570 divisible by 23?
  39. 39.Is 9255 divisible by 7?
  40. 40.Is 116140 divisible by 20?

Answer key

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

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