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Divisibility Rules Worksheet

Vedic maths trick 13: Divisibility tests · Set 703 · 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 50128 divisible by 8?
  2. 2.Is 12934 divisible by 2?
  3. 3.Is 161458 divisible by 24?
  4. 4.Is 4628 divisible by 13?
  5. 5.Is 109980 divisible by 29?
  6. 6.Is 31141 divisible by 6?
  7. 7.Is 30137 divisible by 20?
  8. 8.Is 88871 divisible by 18?
  9. 9.Is 5714 divisible by 3?
  10. 10.Is 21669 divisible by 20?
  11. 11.Is 17593 divisible by 9?
  12. 12.Is 121145 divisible by 24?
  13. 13.Is 52988 divisible by 13?
  14. 14.Is 85100 divisible by 20?
  15. 15.Is 100221 divisible by 17?
  16. 16.Is 56772 divisible by 23?
  17. 17.Is 553 divisible by 3?
  18. 18.Is 28272 divisible by 6?
  19. 19.Is 9270 divisible by 2?
  20. 20.Is 104371 divisible by 29?
  21. 21.Is 23148 divisible by 17?
  22. 22.Is 80822 divisible by 23?
  23. 23.Is 5479 divisible by 3?
  24. 24.Is 19199 divisible by 6?
  25. 25.Is 28562 divisible by 7?
  26. 26.Is 7939 divisible by 2?
  27. 27.Is 14680 divisible by 8?
  28. 28.Is 26388 divisible by 6?
  29. 29.Is 36848 divisible by 7?
  30. 30.Is 27216 divisible by 24?
  31. 31.Is 59015 divisible by 29?
  32. 32.Is 124722 divisible by 18?
  33. 33.Is 25090 divisible by 13?
  34. 34.Is 7301 divisible by 4?
  35. 35.Is 19764 divisible by 9?
  36. 36.Is 13639 divisible by 10?
  37. 37.Is 19745 divisible by 4?
  38. 38.Is 26158 divisible by 9?
  39. 39.Is 66990 divisible by 29?
  40. 40.Is 57222 divisible by 17?

Answer key

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

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