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Divisibility Rules Worksheet

Vedic maths trick 13: Divisibility tests · Set 713 · 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 1999 divisible by 2?
  2. 2.Is 55707 divisible by 9?
  3. 3.Is 97845 divisible by 29?
  4. 4.Is 77877 divisible by 17?
  5. 5.Is 59202 divisible by 9?
  6. 6.Is 91180 divisible by 20?
  7. 7.Is 182160 divisible by 30?
  8. 8.Is 17885 divisible by 9?
  9. 9.Is 40315 divisible by 11?
  10. 10.Is 84550 divisible by 19?
  11. 11.Is 101851 divisible by 15?
  12. 12.Is 78223 divisible by 19?
  13. 13.Is 43217 divisible by 23?
  14. 14.Is 113643 divisible by 23?
  15. 15.Is 30710 divisible by 18?
  16. 16.Is 44143 divisible by 11?
  17. 17.Is 7245 divisible by 5?
  18. 18.Is 98517 divisible by 15?
  19. 19.Is 81603 divisible by 19?
  20. 20.Is 1922 divisible by 3?
  21. 21.Is 28138 divisible by 5?
  22. 22.Is 5137 divisible by 3?
  23. 23.Is 10973 divisible by 5?
  24. 24.Is 21943 divisible by 6?
  25. 25.Is 82870 divisible by 19?
  26. 26.Is 14060 divisible by 3?
  27. 27.Is 48132 divisible by 7?
  28. 28.Is 44441 divisible by 19?
  29. 29.Is 117325 divisible by 17?
  30. 30.Is 13530 divisible by 12?
  31. 31.Is 74312 divisible by 20?
  32. 32.Is 78672 divisible by 24?
  33. 33.Is 8700 divisible by 3?
  34. 34.Is 99265 divisible by 17?
  35. 35.Is 62689 divisible by 11?
  36. 36.Is 83032 divisible by 12?
  37. 37.Is 7460 divisible by 6?
  38. 38.Is 100237 divisible by 23?
  39. 39.Is 64560 divisible by 20?
  40. 40.Is 2139 divisible by 4?

Answer key

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

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