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Divisibility Rules Worksheet

Vedic maths trick 13: Divisibility tests · Set 231 · 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 16695 divisible by 3?
  2. 2.Is 41824 divisible by 24?
  3. 3.Is 8966 divisible by 10?
  4. 4.Is 27072 divisible by 5?
  5. 5.Is 12213 divisible by 9?
  6. 6.Is 96673 divisible by 23?
  7. 7.Is 69253 divisible by 29?
  8. 8.Is 28193 divisible by 13?
  9. 9.Is 3448 divisible by 8?
  10. 10.Is 21791 divisible by 7?
  11. 11.Is 11344 divisible by 4?
  12. 12.Is 2314 divisible by 2?
  13. 13.Is 24879 divisible by 10?
  14. 14.Is 4939 divisible by 15?
  15. 15.Is 102562 divisible by 18?
  16. 16.Is 59793 divisible by 19?
  17. 17.Is 32906 divisible by 5?
  18. 18.Is 33078 divisible by 6?
  19. 19.Is 29967 divisible by 12?
  20. 20.Is 26901 divisible by 6?
  21. 21.Is 74955 divisible by 20?
  22. 22.Is 57438 divisible by 9?
  23. 23.Is 69819 divisible by 17?
  24. 24.Is 29673 divisible by 7?
  25. 25.Is 61712 divisible by 19?
  26. 26.Is 54612 divisible by 12?
  27. 27.Is 75708 divisible by 18?
  28. 28.Is 144870 divisible by 30?
  29. 29.Is 39277 divisible by 6?
  30. 30.Is 1489 divisible by 8?
  31. 31.Is 40859 divisible by 7?
  32. 32.Is 7209 divisible by 3?
  33. 33.Is 11601 divisible by 4?
  34. 34.Is 41610 divisible by 6?
  35. 35.Is 3150 divisible by 4?
  36. 36.Is 12882 divisible by 23?
  37. 37.Is 45951 divisible by 17?
  38. 38.Is 102744 divisible by 18?
  39. 39.Is 46955 divisible by 23?
  40. 40.Is 17089 divisible by 6?

Answer key

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

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