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Divisibility Rules Worksheet

Vedic maths trick 13: Divisibility tests · Set 435 · 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 26744 divisible by 8?
  2. 2.Is 150196 divisible by 29?
  3. 3.Is 24468 divisible by 6?
  4. 4.Is 112347 divisible by 19?
  5. 5.Is 22920 divisible by 24?
  6. 6.Is 64609 divisible by 23?
  7. 7.Is 18988 divisible by 5?
  8. 8.Is 32107 divisible by 7?
  9. 9.Is 12601 divisible by 3?
  10. 10.Is 46207 divisible by 7?
  11. 11.Is 119516 divisible by 19?
  12. 12.Is 16866 divisible by 6?
  13. 13.Is 100483 divisible by 17?
  14. 14.Is 32858 divisible by 11?
  15. 15.Is 38386 divisible by 17?
  16. 16.Is 80170 divisible by 17?
  17. 17.Is 17403 divisible by 3?
  18. 18.Is 99246 divisible by 17?
  19. 19.Is 10164 divisible by 23?
  20. 20.Is 2967 divisible by 8?
  21. 21.Is 18476 divisible by 6?
  22. 22.Is 114025 divisible by 19?
  23. 23.Is 79272 divisible by 12?
  24. 24.Is 4395 divisible by 15?
  25. 25.Is 6415 divisible by 5?
  26. 26.Is 18061 divisible by 6?
  27. 27.Is 26433 divisible by 6?
  28. 28.Is 2088 divisible by 24?
  29. 29.Is 40269 divisible by 12?
  30. 30.Is 113617 divisible by 29?
  31. 31.Is 14327 divisible by 3?
  32. 32.Is 19100 divisible by 10?
  33. 33.Is 38720 divisible by 8?
  34. 34.Is 78957 divisible by 20?
  35. 35.Is 35567 divisible by 20?
  36. 36.Is 11856 divisible by 12?
  37. 37.Is 29185 divisible by 20?
  38. 38.Is 4224 divisible by 12?
  39. 39.Is 61836 divisible by 12?
  40. 40.Is 126000 divisible by 20?

Answer key

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

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