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Divisibility Rules Worksheet

Vedic maths trick 13: Divisibility tests · Set 461 · 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 124984 divisible by 18?
  2. 2.Is 36000 divisible by 13?
  3. 3.Is 24949 divisible by 11?
  4. 4.Is 141205 divisible by 23?
  5. 5.Is 96390 divisible by 19?
  6. 6.Is 6216 divisible by 2?
  7. 7.Is 14620 divisible by 4?
  8. 8.Is 5237 divisible by 2?
  9. 9.Is 22895 divisible by 5?
  10. 10.Is 18090 divisible by 3?
  11. 11.Is 34944 divisible by 18?
  12. 12.Is 73624 divisible by 13?
  13. 13.Is 10625 divisible by 2?
  14. 14.Is 34232 divisible by 11?
  15. 15.Is 48544 divisible by 13?
  16. 16.Is 41769 divisible by 17?
  17. 17.Is 3035 divisible by 2?
  18. 18.Is 109600 divisible by 20?
  19. 19.Is 40735 divisible by 6?
  20. 20.Is 77385 divisible by 15?
  21. 21.Is 110177 divisible by 17?
  22. 22.Is 6677 divisible by 8?
  23. 23.Is 25573 divisible by 29?
  24. 24.Is 20247 divisible by 10?
  25. 25.Is 6000 divisible by 30?
  26. 26.Is 12071 divisible by 5?
  27. 27.Is 33819 divisible by 15?
  28. 28.Is 126347 divisible by 19?
  29. 29.Is 29828 divisible by 29?
  30. 30.Is 1716 divisible by 7?
  31. 31.Is 11643 divisible by 3?
  32. 32.Is 49016 divisible by 11?
  33. 33.Is 15958 divisible by 20?
  34. 34.Is 16446 divisible by 10?
  35. 35.Is 9499 divisible by 5?
  36. 36.Is 31073 divisible by 5?
  37. 37.Is 20395 divisible by 6?
  38. 38.Is 65616 divisible by 24?
  39. 39.Is 46980 divisible by 29?
  40. 40.Is 116229 divisible by 17?

Answer key

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

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