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Divisibility Rules Worksheet

Vedic maths trick 13: Divisibility tests · Set 823 · 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 43990 divisible by 18?
  2. 2.Is 852 divisible by 12?
  3. 3.Is 12720 divisible by 3?
  4. 4.Is 8048 divisible by 2?
  5. 5.Is 58581 divisible by 10?
  6. 6.Is 11418 divisible by 3?
  7. 7.Is 36577 divisible by 18?
  8. 8.Is 50921 divisible by 13?
  9. 9.Is 34830 divisible by 8?
  10. 10.Is 28998 divisible by 18?
  11. 11.Is 3105 divisible by 15?
  12. 12.Is 23868 divisible by 4?
  13. 13.Is 115180 divisible by 20?
  14. 14.Is 106053 divisible by 23?
  15. 15.Is 14184 divisible by 15?
  16. 16.Is 24913 divisible by 7?
  17. 17.Is 3093 divisible by 3?
  18. 18.Is 7134 divisible by 6?
  19. 19.Is 37745 divisible by 6?
  20. 20.Is 12205 divisible by 2?
  21. 21.Is 29328 divisible by 6?
  22. 22.Is 54983 divisible by 17?
  23. 23.Is 105621 divisible by 19?
  24. 24.Is 13143 divisible by 18?
  25. 25.Is 761 divisible by 24?
  26. 26.Is 6138 divisible by 2?
  27. 27.Is 7395 divisible by 5?
  28. 28.Is 11895 divisible by 13?
  29. 29.Is 60410 divisible by 12?
  30. 30.Is 13839 divisible by 5?
  31. 31.Is 157206 divisible by 24?
  32. 32.Is 147720 divisible by 24?
  33. 33.Is 18336 divisible by 24?
  34. 34.Is 62213 divisible by 15?
  35. 35.Is 61830 divisible by 9?
  36. 36.Is 56050 divisible by 11?
  37. 37.Is 140763 divisible by 23?
  38. 38.Is 19822 divisible by 11?
  39. 39.Is 37143 divisible by 6?
  40. 40.Is 1748 divisible by 23?

Answer key

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

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