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Divisibility Rules Worksheet

Vedic maths trick 13: Divisibility tests · Set 372 · 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 4235 divisible by 11?
  2. 2.Is 25623 divisible by 13?
  3. 3.Is 41363 divisible by 8?
  4. 4.Is 64220 divisible by 23?
  5. 5.Is 4280 divisible by 5?
  6. 6.Is 37120 divisible by 29?
  7. 7.Is 84722 divisible by 20?
  8. 8.Is 59098 divisible by 12?
  9. 9.Is 36498 divisible by 8?
  10. 10.Is 194 divisible by 2?
  11. 11.Is 23750 divisible by 10?
  12. 12.Is 101315 divisible by 24?
  13. 13.Is 10596 divisible by 5?
  14. 14.Is 11007 divisible by 6?
  15. 15.Is 6812 divisible by 10?
  16. 16.Is 20666 divisible by 3?
  17. 17.Is 12963 divisible by 3?
  18. 18.Is 48028 divisible by 24?
  19. 19.Is 8692 divisible by 7?
  20. 20.Is 41310 divisible by 30?
  21. 21.Is 153359 divisible by 23?
  22. 22.Is 94969 divisible by 23?
  23. 23.Is 61159 divisible by 9?
  24. 24.Is 44232 divisible by 19?
  25. 25.Is 3287 divisible by 2?
  26. 26.Is 12207 divisible by 12?
  27. 27.Is 597 divisible by 2?
  28. 28.Is 59166 divisible by 9?
  29. 29.Is 12586 divisible by 2?
  30. 30.Is 45513 divisible by 13?
  31. 31.Is 77017 divisible by 23?
  32. 32.Is 42747 divisible by 11?
  33. 33.Is 2346 divisible by 23?
  34. 34.Is 91506 divisible by 23?
  35. 35.Is 42812 divisible by 15?
  36. 36.Is 74022 divisible by 18?
  37. 37.Is 1983 divisible by 2?
  38. 38.Is 90627 divisible by 30?
  39. 39.Is 29274 divisible by 7?
  40. 40.Is 63432 divisible by 12?

Answer key

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

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