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Divisibility Rules Worksheet

Vedic maths trick 13: Divisibility tests · Set 212 · 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 9852 divisible by 8?
  2. 2.Is 8681 divisible by 9?
  3. 3.Is 25370 divisible by 10?
  4. 4.Is 133791 divisible by 23?
  5. 5.Is 14560 divisible by 10?
  6. 6.Is 40819 divisible by 11?
  7. 7.Is 115671 divisible by 17?
  8. 8.Is 101933 divisible by 17?
  9. 9.Is 9459 divisible by 9?
  10. 10.Is 3650 divisible by 5?
  11. 11.Is 1567 divisible by 6?
  12. 12.Is 42090 divisible by 7?
  13. 13.Is 3080 divisible by 11?
  14. 14.Is 8361 divisible by 3?
  15. 15.Is 37296 divisible by 12?
  16. 16.Is 13706 divisible by 7?
  17. 17.Is 13524 divisible by 6?
  18. 18.Is 297 divisible by 4?
  19. 19.Is 202217 divisible by 29?
  20. 20.Is 4656 divisible by 11?
  21. 21.Is 13495 divisible by 5?
  22. 22.Is 88526 divisible by 18?
  23. 23.Is 61770 divisible by 29?
  24. 24.Is 27421 divisible by 20?
  25. 25.Is 9044 divisible by 17?
  26. 26.Is 30901 divisible by 13?
  27. 27.Is 46954 divisible by 7?
  28. 28.Is 22148 divisible by 7?
  29. 29.Is 9149 divisible by 2?
  30. 30.Is 29030 divisible by 5?
  31. 31.Is 6727 divisible by 4?
  32. 32.Is 86418 divisible by 15?
  33. 33.Is 184319 divisible by 29?
  34. 34.Is 26679 divisible by 17?
  35. 35.Is 36837 divisible by 20?
  36. 36.Is 18379 divisible by 8?
  37. 37.Is 14494 divisible by 6?
  38. 38.Is 6656 divisible by 7?
  39. 39.Is 49535 divisible by 24?
  40. 40.Is 10872 divisible by 3?

Answer key

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

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