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Divisibility Rules Worksheet

Vedic maths trick 13: Divisibility tests · Set 111 · 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 8640 divisible by 6?
  2. 2.Is 32031 divisible by 9?
  3. 3.Is 42690 divisible by 9?
  4. 4.Is 20381 divisible by 4?
  5. 5.Is 176859 divisible by 29?
  6. 6.Is 9302 divisible by 29?
  7. 7.Is 78086 divisible by 29?
  8. 8.Is 16072 divisible by 4?
  9. 9.Is 21648 divisible by 12?
  10. 10.Is 42566 divisible by 20?
  11. 11.Is 4143 divisible by 2?
  12. 12.Is 25041 divisible by 17?
  13. 13.Is 202170 divisible by 30?
  14. 14.Is 60606 divisible by 9?
  15. 15.Is 24898 divisible by 5?
  16. 16.Is 30823 divisible by 13?
  17. 17.Is 183870 divisible by 30?
  18. 18.Is 43134 divisible by 7?
  19. 19.Is 63137 divisible by 19?
  20. 20.Is 9207 divisible by 19?
  21. 21.Is 90540 divisible by 15?
  22. 22.Is 89982 divisible by 13?
  23. 23.Is 93945 divisible by 24?
  24. 24.Is 22884 divisible by 20?
  25. 25.Is 41328 divisible by 15?
  26. 26.Is 34950 divisible by 6?
  27. 27.Is 32173 divisible by 10?
  28. 28.Is 28284 divisible by 12?
  29. 29.Is 16510 divisible by 7?
  30. 30.Is 67328 divisible by 19?
  31. 31.Is 68614 divisible by 15?
  32. 32.Is 15426 divisible by 10?
  33. 33.Is 70524 divisible by 18?
  34. 34.Is 44975 divisible by 7?
  35. 35.Is 19269 divisible by 4?
  36. 36.Is 19425 divisible by 15?
  37. 37.Is 12519 divisible by 13?
  38. 38.Is 113777 divisible by 17?
  39. 39.Is 10894 divisible by 6?
  40. 40.Is 50736 divisible by 12?

Answer key

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

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