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Divisibility Rules Worksheet

Vedic maths trick 13: Divisibility tests · Set 112 · 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 9993 divisible by 3?
  2. 2.Is 6993 divisible by 2?
  3. 3.Is 148224 divisible by 24?
  4. 4.Is 1300 divisible by 9?
  5. 5.Is 6680 divisible by 10?
  6. 6.Is 23545 divisible by 5?
  7. 7.Is 52456 divisible by 29?
  8. 8.Is 37638 divisible by 17?
  9. 9.Is 100650 divisible by 15?
  10. 10.Is 39668 divisible by 12?
  11. 11.Is 13263 divisible by 6?
  12. 12.Is 32372 divisible by 7?
  13. 13.Is 17618 divisible by 17?
  14. 14.Is 10028 divisible by 5?
  15. 15.Is 124773 divisible by 30?
  16. 16.Is 106053 divisible by 29?
  17. 17.Is 3414 divisible by 17?
  18. 18.Is 106802 divisible by 29?
  19. 19.Is 8965 divisible by 11?
  20. 20.Is 65040 divisible by 15?
  21. 21.Is 34940 divisible by 6?
  22. 22.Is 81354 divisible by 18?
  23. 23.Is 186934 divisible by 29?
  24. 24.Is 127006 divisible by 23?
  25. 25.Is 4375 divisible by 2?
  26. 26.Is 17976 divisible by 6?
  27. 27.Is 48333 divisible by 11?
  28. 28.Is 40014 divisible by 9?
  29. 29.Is 42999 divisible by 11?
  30. 30.Is 57494 divisible by 30?
  31. 31.Is 41621 divisible by 9?
  32. 32.Is 6450 divisible by 15?
  33. 33.Is 120265 divisible by 18?
  34. 34.Is 28734 divisible by 17?
  35. 35.Is 4126 divisible by 6?
  36. 36.Is 27775 divisible by 8?
  37. 37.Is 3911 divisible by 3?
  38. 38.Is 103212 divisible by 18?
  39. 39.Is 496 divisible by 23?
  40. 40.Is 53828 divisible by 11?

Answer key

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

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