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Divisibility Rules Worksheet

Vedic maths trick 13: Divisibility tests · Set 443 · 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 37142 divisible by 7?
  2. 2.Is 140767 divisible by 30?
  3. 3.Is 11046 divisible by 5?
  4. 4.Is 36415 divisible by 13?
  5. 5.Is 33908 divisible by 7?
  6. 6.Is 17325 divisible by 3?
  7. 7.Is 21732 divisible by 20?
  8. 8.Is 7072 divisible by 7?
  9. 9.Is 82710 divisible by 24?
  10. 10.Is 11033 divisible by 8?
  11. 11.Is 8695 divisible by 3?
  12. 12.Is 26191 divisible by 8?
  13. 13.Is 3768 divisible by 8?
  14. 14.Is 40808 divisible by 8?
  15. 15.Is 22300 divisible by 5?
  16. 16.Is 46470 divisible by 10?
  17. 17.Is 12892 divisible by 11?
  18. 18.Is 47538 divisible by 18?
  19. 19.Is 16252 divisible by 17?
  20. 20.Is 48354 divisible by 12?
  21. 21.Is 24572 divisible by 30?
  22. 22.Is 61933 divisible by 30?
  23. 23.Is 55946 divisible by 8?
  24. 24.Is 18061 divisible by 9?
  25. 25.Is 18840 divisible by 4?
  26. 26.Is 9837 divisible by 9?
  27. 27.Is 20850 divisible by 15?
  28. 28.Is 80412 divisible by 12?
  29. 29.Is 84556 divisible by 15?
  30. 30.Is 26951 divisible by 8?
  31. 31.Is 14487 divisible by 10?
  32. 32.Is 18305 divisible by 3?
  33. 33.Is 44550 divisible by 15?
  34. 34.Is 66369 divisible by 17?
  35. 35.Is 41943 divisible by 10?
  36. 36.Is 16694 divisible by 9?
  37. 37.Is 2165 divisible by 12?
  38. 38.Is 86823 divisible by 15?
  39. 39.Is 81136 divisible by 13?
  40. 40.Is 2782 divisible by 2?

Answer key

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

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