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Divisibility Rules Worksheet

Vedic maths trick 13: Divisibility tests · Set 201 · 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 36811 divisible by 23?
  2. 2.Is 27857 divisible by 12?
  3. 3.Is 41318 divisible by 30?
  4. 4.Is 9870 divisible by 4?
  5. 5.Is 15263 divisible by 5?
  6. 6.Is 41793 divisible by 9?
  7. 7.Is 40623 divisible by 7?
  8. 8.Is 13243 divisible by 3?
  9. 9.Is 1921 divisible by 3?
  10. 10.Is 91472 divisible by 17?
  11. 11.Is 26371 divisible by 9?
  12. 12.Is 10829 divisible by 4?
  13. 13.Is 125213 divisible by 29?
  14. 14.Is 85251 divisible by 20?
  15. 15.Is 22371 divisible by 18?
  16. 16.Is 14047 divisible by 12?
  17. 17.Is 3832 divisible by 8?
  18. 18.Is 100786 divisible by 29?
  19. 19.Is 56397 divisible by 11?
  20. 20.Is 107109 divisible by 30?
  21. 21.Is 95171 divisible by 19?
  22. 22.Is 88074 divisible by 30?
  23. 23.Is 14647 divisible by 19?
  24. 24.Is 4900 divisible by 10?
  25. 25.Is 28507 divisible by 8?
  26. 26.Is 78872 divisible by 20?
  27. 27.Is 22768 divisible by 7?
  28. 28.Is 41413 divisible by 30?
  29. 29.Is 63972 divisible by 12?
  30. 30.Is 4898 divisible by 6?
  31. 31.Is 37176 divisible by 12?
  32. 32.Is 11988 divisible by 4?
  33. 33.Is 39677 divisible by 24?
  34. 34.Is 7861 divisible by 3?
  35. 35.Is 14820 divisible by 12?
  36. 36.Is 55110 divisible by 18?
  37. 37.Is 27440 divisible by 8?
  38. 38.Is 12339 divisible by 19?
  39. 39.Is 15780 divisible by 20?
  40. 40.Is 89730 divisible by 15?

Answer key

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

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