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Divisibility Rules Worksheet

Vedic maths trick 13: Divisibility tests · Set 562 · 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 4402 divisible by 4?
  2. 2.Is 13082 divisible by 2?
  3. 3.Is 39500 divisible by 9?
  4. 4.Is 16880 divisible by 20?
  5. 5.Is 31764 divisible by 7?
  6. 6.Is 28205 divisible by 7?
  7. 7.Is 28159 divisible by 6?
  8. 8.Is 90022 divisible by 23?
  9. 9.Is 6013 divisible by 7?
  10. 10.Is 46460 divisible by 15?
  11. 11.Is 809 divisible by 7?
  12. 12.Is 14718 divisible by 4?
  13. 13.Is 124526 divisible by 19?
  14. 14.Is 36710 divisible by 29?
  15. 15.Is 47831 divisible by 7?
  16. 16.Is 25545 divisible by 8?
  17. 17.Is 58805 divisible by 12?
  18. 18.Is 96048 divisible by 18?
  19. 19.Is 37608 divisible by 6?
  20. 20.Is 37988 divisible by 8?
  21. 21.Is 143 divisible by 3?
  22. 22.Is 39519 divisible by 20?
  23. 23.Is 9418 divisible by 17?
  24. 24.Is 11046 divisible by 3?
  25. 25.Is 28755 divisible by 19?
  26. 26.Is 2520 divisible by 15?
  27. 27.Is 78198 divisible by 17?
  28. 28.Is 75465 divisible by 24?
  29. 29.Is 108358 divisible by 30?
  30. 30.Is 66236 divisible by 29?
  31. 31.Is 42780 divisible by 15?
  32. 32.Is 13248 divisible by 12?
  33. 33.Is 11259 divisible by 2?
  34. 34.Is 52681 divisible by 8?
  35. 35.Is 96491 divisible by 18?
  36. 36.Is 15157 divisible by 23?
  37. 37.Is 55966 divisible by 17?
  38. 38.Is 77561 divisible by 15?
  39. 39.Is 2500 divisible by 10?
  40. 40.Is 80316 divisible by 12?

Answer key

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

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