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Divisibility Rules Worksheet

Vedic maths trick 13: Divisibility tests · Set 334 · 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 51230 divisible by 10?
  2. 2.Is 104099 divisible by 29?
  3. 3.Is 3280 divisible by 10?
  4. 4.Is 79551 divisible by 23?
  5. 5.Is 27810 divisible by 15?
  6. 6.Is 21507 divisible by 10?
  7. 7.Is 86610 divisible by 30?
  8. 8.Is 34904 divisible by 18?
  9. 9.Is 10204 divisible by 2?
  10. 10.Is 85874 divisible by 18?
  11. 11.Is 8628 divisible by 4?
  12. 12.Is 22980 divisible by 20?
  13. 13.Is 79548 divisible by 13?
  14. 14.Is 69458 divisible by 19?
  15. 15.Is 8684 divisible by 3?
  16. 16.Is 6288 divisible by 6?
  17. 17.Is 112744 divisible by 24?
  18. 18.Is 20174 divisible by 7?
  19. 19.Is 15137 divisible by 3?
  20. 20.Is 88701 divisible by 15?
  21. 21.Is 57992 divisible by 11?
  22. 22.Is 22321 divisible by 17?
  23. 23.Is 150456 divisible by 24?
  24. 24.Is 7429 divisible by 7?
  25. 25.Is 75840 divisible by 15?
  26. 26.Is 65740 divisible by 23?
  27. 27.Is 8762 divisible by 4?
  28. 28.Is 74469 divisible by 12?
  29. 29.Is 98190 divisible by 30?
  30. 30.Is 95404 divisible by 23?
  31. 31.Is 86323 divisible by 13?
  32. 32.Is 69029 divisible by 11?
  33. 33.Is 37020 divisible by 30?
  34. 34.Is 33072 divisible by 6?
  35. 35.Is 31242 divisible by 6?
  36. 36.Is 30742 divisible by 19?
  37. 37.Is 30412 divisible by 9?
  38. 38.Is 1107 divisible by 7?
  39. 39.Is 12961 divisible by 7?
  40. 40.Is 14401 divisible by 3?

Answer key

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

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