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Divisibility Rules Worksheet

Vedic maths trick 13: Divisibility tests · Set 466 · 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 40435 divisible by 7?
  2. 2.Is 155963 divisible by 23?
  3. 3.Is 27788 divisible by 5?
  4. 4.Is 22696 divisible by 9?
  5. 5.Is 51582 divisible by 13?
  6. 6.Is 202950 divisible by 30?
  7. 7.Is 45163 divisible by 10?
  8. 8.Is 49983 divisible by 8?
  9. 9.Is 19867 divisible by 8?
  10. 10.Is 100297 divisible by 19?
  11. 11.Is 3862 divisible by 7?
  12. 12.Is 78650 divisible by 15?
  13. 13.Is 55595 divisible by 12?
  14. 14.Is 6092 divisible by 2?
  15. 15.Is 62943 divisible by 9?
  16. 16.Is 8263 divisible by 3?
  17. 17.Is 150972 divisible by 23?
  18. 18.Is 15244 divisible by 12?
  19. 19.Is 117384 divisible by 24?
  20. 20.Is 98022 divisible by 17?
  21. 21.Is 21957 divisible by 9?
  22. 22.Is 42960 divisible by 8?
  23. 23.Is 35743 divisible by 18?
  24. 24.Is 12810 divisible by 7?
  25. 25.Is 471 divisible by 4?
  26. 26.Is 96181 divisible by 24?
  27. 27.Is 20469 divisible by 5?
  28. 28.Is 22870 divisible by 10?
  29. 29.Is 36968 divisible by 23?
  30. 30.Is 3515 divisible by 19?
  31. 31.Is 40156 divisible by 7?
  32. 32.Is 97324 divisible by 29?
  33. 33.Is 83651 divisible by 12?
  34. 34.Is 161925 divisible by 24?
  35. 35.Is 8952 divisible by 8?
  36. 36.Is 45220 divisible by 20?
  37. 37.Is 96231 divisible by 19?
  38. 38.Is 11440 divisible by 4?
  39. 39.Is 32596 divisible by 29?
  40. 40.Is 2663 divisible by 2?

Answer key

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

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