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Divisibility Rules Worksheet

Vedic maths trick 13: Divisibility tests · Set 307 · 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 37262 divisible by 10?
  2. 2.Is 46852 divisible by 17?
  3. 3.Is 9821 divisible by 7?
  4. 4.Is 180011 divisible by 30?
  5. 5.Is 21591 divisible by 7?
  6. 6.Is 28849 divisible by 7?
  7. 7.Is 10225 divisible by 2?
  8. 8.Is 26332 divisible by 29?
  9. 9.Is 72197 divisible by 19?
  10. 10.Is 68880 divisible by 15?
  11. 11.Is 24523 divisible by 7?
  12. 12.Is 24680 divisible by 18?
  13. 13.Is 9571 divisible by 7?
  14. 14.Is 9064 divisible by 8?
  15. 15.Is 8422 divisible by 6?
  16. 16.Is 36776 divisible by 8?
  17. 17.Is 42150 divisible by 23?
  18. 18.Is 786 divisible by 2?
  19. 19.Is 24771 divisible by 23?
  20. 20.Is 86683 divisible by 18?
  21. 21.Is 33170 divisible by 10?
  22. 22.Is 26652 divisible by 6?
  23. 23.Is 861 divisible by 7?
  24. 24.Is 12036 divisible by 6?
  25. 25.Is 9047 divisible by 3?
  26. 26.Is 50280 divisible by 20?
  27. 27.Is 97620 divisible by 30?
  28. 28.Is 93798 divisible by 24?
  29. 29.Is 34165 divisible by 7?
  30. 30.Is 92655 divisible by 15?
  31. 31.Is 1573 divisible by 11?
  32. 32.Is 48374 divisible by 19?
  33. 33.Is 27635 divisible by 4?
  34. 34.Is 14867 divisible by 7?
  35. 35.Is 37209 divisible by 12?
  36. 36.Is 32027 divisible by 12?
  37. 37.Is 12464 divisible by 8?
  38. 38.Is 17839 divisible by 18?
  39. 39.Is 68471 divisible by 23?
  40. 40.Is 39797 divisible by 23?

Answer key

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

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