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Divisibility Rules Worksheet

Vedic maths trick 13: Divisibility tests · Set 774 · 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 20716 divisible by 4?
  2. 2.Is 104306 divisible by 15?
  3. 3.Is 27799 divisible by 7?
  4. 4.Is 83474 divisible by 23?
  5. 5.Is 21190 divisible by 13?
  6. 6.Is 73943 divisible by 20?
  7. 7.Is 14880 divisible by 7?
  8. 8.Is 151773 divisible by 29?
  9. 9.Is 22492 divisible by 13?
  10. 10.Is 13896 divisible by 2?
  11. 11.Is 12546 divisible by 5?
  12. 12.Is 57250 divisible by 15?
  13. 13.Is 22373 divisible by 13?
  14. 14.Is 34777 divisible by 5?
  15. 15.Is 4502 divisible by 2?
  16. 16.Is 155158 divisible by 23?
  17. 17.Is 27795 divisible by 15?
  18. 18.Is 17856 divisible by 6?
  19. 19.Is 7464 divisible by 2?
  20. 20.Is 21229 divisible by 12?
  21. 21.Is 137101 divisible by 24?
  22. 22.Is 3517 divisible by 2?
  23. 23.Is 45120 divisible by 10?
  24. 24.Is 3181 divisible by 30?
  25. 25.Is 26572 divisible by 13?
  26. 26.Is 12486 divisible by 12?
  27. 27.Is 38127 divisible by 29?
  28. 28.Is 46846 divisible by 7?
  29. 29.Is 39468 divisible by 6?
  30. 30.Is 4403 divisible by 7?
  31. 31.Is 7753 divisible by 15?
  32. 32.Is 38528 divisible by 7?
  33. 33.Is 14917 divisible by 19?
  34. 34.Is 115293 divisible by 24?
  35. 35.Is 109641 divisible by 20?
  36. 36.Is 5126 divisible by 8?
  37. 37.Is 9650 divisible by 18?
  38. 38.Is 12960 divisible by 24?
  39. 39.Is 84445 divisible by 30?
  40. 40.Is 68580 divisible by 30?

Answer key

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

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