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Divisibility Rules Worksheet

Vedic maths trick 13: Divisibility tests · Set 414 · 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 38760 divisible by 6?
  2. 2.Is 3246 divisible by 6?
  3. 3.Is 21110 divisible by 12?
  4. 4.Is 66782 divisible by 17?
  5. 5.Is 8838 divisible by 6?
  6. 6.Is 27420 divisible by 12?
  7. 7.Is 6642 divisible by 2?
  8. 8.Is 22542 divisible by 12?
  9. 9.Is 156814 divisible by 23?
  10. 10.Is 16208 divisible by 3?
  11. 11.Is 68929 divisible by 17?
  12. 12.Is 10566 divisible by 20?
  13. 13.Is 52193 divisible by 19?
  14. 14.Is 55039 divisible by 17?
  15. 15.Is 22392 divisible by 18?
  16. 16.Is 87853 divisible by 15?
  17. 17.Is 9781 divisible by 2?
  18. 18.Is 6677 divisible by 2?
  19. 19.Is 41575 divisible by 19?
  20. 20.Is 69311 divisible by 17?
  21. 21.Is 7062 divisible by 5?
  22. 22.Is 18632 divisible by 8?
  23. 23.Is 22419 divisible by 9?
  24. 24.Is 30800 divisible by 5?
  25. 25.Is 9290 divisible by 19?
  26. 26.Is 15837 divisible by 10?
  27. 27.Is 36080 divisible by 7?
  28. 28.Is 5849 divisible by 2?
  29. 29.Is 75816 divisible by 13?
  30. 30.Is 89136 divisible by 13?
  31. 31.Is 90885 divisible by 15?
  32. 32.Is 33509 divisible by 7?
  33. 33.Is 1110 divisible by 6?
  34. 34.Is 48372 divisible by 17?
  35. 35.Is 49080 divisible by 10?
  36. 36.Is 66165 divisible by 15?
  37. 37.Is 53714 divisible by 8?
  38. 38.Is 26440 divisible by 4?
  39. 39.Is 4272 divisible by 6?
  40. 40.Is 51381 divisible by 23?

Answer key

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

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