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Divisibility Rules Worksheet

Vedic maths trick 13: Divisibility tests · Set 996 · 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 11228 divisible by 23?
  2. 2.Is 47514 divisible by 12?
  3. 3.Is 41140 divisible by 17?
  4. 4.Is 11864 divisible by 3?
  5. 5.Is 176477 divisible by 29?
  6. 6.Is 14100 divisible by 15?
  7. 7.Is 19057 divisible by 4?
  8. 8.Is 54038 divisible by 9?
  9. 9.Is 18805 divisible by 5?
  10. 10.Is 13554 divisible by 18?
  11. 11.Is 2578 divisible by 6?
  12. 12.Is 44513 divisible by 7?
  13. 13.Is 7452 divisible by 2?
  14. 14.Is 34636 divisible by 5?
  15. 15.Is 49856 divisible by 19?
  16. 16.Is 20002 divisible by 5?
  17. 17.Is 56900 divisible by 10?
  18. 18.Is 19836 divisible by 5?
  19. 19.Is 10873 divisible by 13?
  20. 20.Is 27968 divisible by 19?
  21. 21.Is 13620 divisible by 30?
  22. 22.Is 13696 divisible by 12?
  23. 23.Is 19200 divisible by 15?
  24. 24.Is 18216 divisible by 9?
  25. 25.Is 16290 divisible by 15?
  26. 26.Is 6176 divisible by 4?
  27. 27.Is 12198 divisible by 7?
  28. 28.Is 29111 divisible by 8?
  29. 29.Is 17383 divisible by 3?
  30. 30.Is 2417 divisible by 9?
  31. 31.Is 27368 divisible by 11?
  32. 32.Is 66970 divisible by 10?
  33. 33.Is 8067 divisible by 6?
  34. 34.Is 132298 divisible by 29?
  35. 35.Is 30640 divisible by 8?
  36. 36.Is 13543 divisible by 10?
  37. 37.Is 62145 divisible by 15?
  38. 38.Is 112859 divisible by 24?
  39. 39.Is 9183 divisible by 11?
  40. 40.Is 460 divisible by 3?

Answer key

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

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