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Divisibility Rules Worksheet

Vedic maths trick 13: Divisibility tests · Set 13 · 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 129886 divisible by 19?
  2. 2.Is 6924 divisible by 2?
  3. 3.Is 11082 divisible by 6?
  4. 4.Is 8131 divisible by 5?
  5. 5.Is 113569 divisible by 23?
  6. 6.Is 57793 divisible by 19?
  7. 7.Is 71280 divisible by 12?
  8. 8.Is 15870 divisible by 7?
  9. 9.Is 110620 divisible by 20?
  10. 10.Is 11248 divisible by 10?
  11. 11.Is 41590 divisible by 13?
  12. 12.Is 62529 divisible by 19?
  13. 13.Is 22258 divisible by 5?
  14. 14.Is 75985 divisible by 18?
  15. 15.Is 45807 divisible by 23?
  16. 16.Is 8897 divisible by 5?
  17. 17.Is 33839 divisible by 13?
  18. 18.Is 6569 divisible by 5?
  19. 19.Is 25892 divisible by 11?
  20. 20.Is 9268 divisible by 7?
  21. 21.Is 83943 divisible by 17?
  22. 22.Is 1072 divisible by 3?
  23. 23.Is 55199 divisible by 12?
  24. 24.Is 137067 divisible by 24?
  25. 25.Is 51143 divisible by 8?
  26. 26.Is 17176 divisible by 19?
  27. 27.Is 87372 divisible by 29?
  28. 28.Is 27797 divisible by 4?
  29. 29.Is 13171 divisible by 2?
  30. 30.Is 8381 divisible by 2?
  31. 31.Is 62084 divisible by 17?
  32. 32.Is 101007 divisible by 29?
  33. 33.Is 104904 divisible by 24?
  34. 34.Is 44740 divisible by 8?
  35. 35.Is 75566 divisible by 23?
  36. 36.Is 117779 divisible by 17?
  37. 37.Is 10440 divisible by 3?
  38. 38.Is 4663 divisible by 11?
  39. 39.Is 33960 divisible by 20?
  40. 40.Is 3307 divisible by 30?

Answer key

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

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