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Divisibility Rules Worksheet

Vedic maths trick 13: Divisibility tests · Set 535 · 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 16429 divisible by 3?
  2. 2.Is 35806 divisible by 17?
  3. 3.Is 34986 divisible by 13?
  4. 4.Is 65729 divisible by 17?
  5. 5.Is 26761 divisible by 19?
  6. 6.Is 34744 divisible by 8?
  7. 7.Is 21835 divisible by 5?
  8. 8.Is 25918 divisible by 6?
  9. 9.Is 1240 divisible by 5?
  10. 10.Is 89453 divisible by 17?
  11. 11.Is 43481 divisible by 18?
  12. 12.Is 5757 divisible by 4?
  13. 13.Is 31911 divisible by 5?
  14. 14.Is 110791 divisible by 23?
  15. 15.Is 132071 divisible by 30?
  16. 16.Is 33054 divisible by 5?
  17. 17.Is 36054 divisible by 9?
  18. 18.Is 48718 divisible by 12?
  19. 19.Is 38500 divisible by 11?
  20. 20.Is 3225 divisible by 2?
  21. 21.Is 47201 divisible by 18?
  22. 22.Is 69276 divisible by 12?
  23. 23.Is 5046 divisible by 29?
  24. 24.Is 88088 divisible by 13?
  25. 25.Is 29560 divisible by 10?
  26. 26.Is 15682 divisible by 3?
  27. 27.Is 28912 divisible by 7?
  28. 28.Is 87375 divisible by 24?
  29. 29.Is 25076 divisible by 4?
  30. 30.Is 18160 divisible by 4?
  31. 31.Is 77879 divisible by 24?
  32. 32.Is 30264 divisible by 6?
  33. 33.Is 56445 divisible by 15?
  34. 34.Is 11410 divisible by 15?
  35. 35.Is 10107 divisible by 3?
  36. 36.Is 130368 divisible by 24?
  37. 37.Is 66750 divisible by 30?
  38. 38.Is 6118 divisible by 4?
  39. 39.Is 100625 divisible by 23?
  40. 40.Is 116585 divisible by 20?

Answer key

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

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