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Divisibility Rules Worksheet

Vedic maths trick 13: Divisibility tests · Set 167 · 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 69614 divisible by 18?
  2. 2.Is 58100 divisible by 20?
  3. 3.Is 287 divisible by 7?
  4. 4.Is 1023 divisible by 11?
  5. 5.Is 18323 divisible by 8?
  6. 6.Is 4518 divisible by 6?
  7. 7.Is 61894 divisible by 20?
  8. 8.Is 102426 divisible by 20?
  9. 9.Is 32381 divisible by 5?
  10. 10.Is 164724 divisible by 29?
  11. 11.Is 90972 divisible by 17?
  12. 12.Is 34973 divisible by 5?
  13. 13.Is 95608 divisible by 17?
  14. 14.Is 9792 divisible by 8?
  15. 15.Is 5280 divisible by 3?
  16. 16.Is 16552 divisible by 29?
  17. 17.Is 106198 divisible by 29?
  18. 18.Is 95817 divisible by 30?
  19. 19.Is 23997 divisible by 19?
  20. 20.Is 5220 divisible by 5?
  21. 21.Is 22729 divisible by 17?
  22. 22.Is 201568 divisible by 29?
  23. 23.Is 90504 divisible by 18?
  24. 24.Is 81016 divisible by 19?
  25. 25.Is 12627 divisible by 3?
  26. 26.Is 75939 divisible by 20?
  27. 27.Is 94078 divisible by 17?
  28. 28.Is 37548 divisible by 7?
  29. 29.Is 800 divisible by 30?
  30. 30.Is 367 divisible by 2?
  31. 31.Is 19186 divisible by 5?
  32. 32.Is 15090 divisible by 3?
  33. 33.Is 17640 divisible by 9?
  34. 34.Is 36408 divisible by 12?
  35. 35.Is 36620 divisible by 8?
  36. 36.Is 17096 divisible by 10?
  37. 37.Is 94050 divisible by 19?
  38. 38.Is 49898 divisible by 13?
  39. 39.Is 138960 divisible by 20?
  40. 40.Is 88272 divisible by 18?

Answer key

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

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