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Divisibility Rules Worksheet

Vedic maths trick 13: Divisibility tests · Set 793 · 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 16110 divisible by 15?
  2. 2.Is 23353 divisible by 5?
  3. 3.Is 86914 divisible by 19?
  4. 4.Is 40590 divisible by 13?
  5. 5.Is 55704 divisible by 23?
  6. 6.Is 20589 divisible by 4?
  7. 7.Is 2969 divisible by 3?
  8. 8.Is 27671 divisible by 4?
  9. 9.Is 11934 divisible by 18?
  10. 10.Is 25734 divisible by 5?
  11. 11.Is 3683 divisible by 29?
  12. 12.Is 55676 divisible by 29?
  13. 13.Is 31056 divisible by 20?
  14. 14.Is 18314 divisible by 6?
  15. 15.Is 3167 divisible by 7?
  16. 16.Is 10155 divisible by 3?
  17. 17.Is 130536 divisible by 24?
  18. 18.Is 109614 divisible by 19?
  19. 19.Is 4592 divisible by 3?
  20. 20.Is 131485 divisible by 24?
  21. 21.Is 117309 divisible by 18?
  22. 22.Is 6257 divisible by 3?
  23. 23.Is 17072 divisible by 8?
  24. 24.Is 20863 divisible by 3?
  25. 25.Is 10232 divisible by 2?
  26. 26.Is 106633 divisible by 29?
  27. 27.Is 63110 divisible by 10?
  28. 28.Is 29493 divisible by 17?
  29. 29.Is 11367 divisible by 5?
  30. 30.Is 19220 divisible by 24?
  31. 31.Is 37332 divisible by 23?
  32. 32.Is 36312 divisible by 8?
  33. 33.Is 98972 divisible by 17?
  34. 34.Is 26966 divisible by 6?
  35. 35.Is 118423 divisible by 30?
  36. 36.Is 72372 divisible by 11?
  37. 37.Is 32479 divisible by 19?
  38. 38.Is 13395 divisible by 23?
  39. 39.Is 443 divisible by 19?
  40. 40.Is 6282 divisible by 5?

Answer key

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

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