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Divisibility Rules Worksheet

Vedic maths trick 13: Divisibility tests · Set 658 · 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 97145 divisible by 20?
  2. 2.Is 10170 divisible by 10?
  3. 3.Is 38374 divisible by 30?
  4. 4.Is 259 divisible by 7?
  5. 5.Is 89666 divisible by 13?
  6. 6.Is 3673 divisible by 5?
  7. 7.Is 4023 divisible by 2?
  8. 8.Is 175166 divisible by 30?
  9. 9.Is 5413 divisible by 3?
  10. 10.Is 6689 divisible by 7?
  11. 11.Is 64125 divisible by 24?
  12. 12.Is 10996 divisible by 15?
  13. 13.Is 19463 divisible by 10?
  14. 14.Is 6648 divisible by 4?
  15. 15.Is 6428 divisible by 2?
  16. 16.Is 67612 divisible by 24?
  17. 17.Is 8248 divisible by 2?
  18. 18.Is 15885 divisible by 15?
  19. 19.Is 19324 divisible by 4?
  20. 20.Is 1692 divisible by 3?
  21. 21.Is 24940 divisible by 19?
  22. 22.Is 24311 divisible by 7?
  23. 23.Is 7034 divisible by 3?
  24. 24.Is 57769 divisible by 20?
  25. 25.Is 3131 divisible by 3?
  26. 26.Is 12122 divisible by 2?
  27. 27.Is 17479 divisible by 11?
  28. 28.Is 74184 divisible by 11?
  29. 29.Is 15991 divisible by 3?
  30. 30.Is 11071 divisible by 13?
  31. 31.Is 68879 divisible by 15?
  32. 32.Is 112747 divisible by 19?
  33. 33.Is 7964 divisible by 6?
  34. 34.Is 20976 divisible by 23?
  35. 35.Is 30915 divisible by 15?
  36. 36.Is 43807 divisible by 7?
  37. 37.Is 17028 divisible by 11?
  38. 38.Is 9057 divisible by 9?
  39. 39.Is 67365 divisible by 15?
  40. 40.Is 209970 divisible by 30?

Answer key

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

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