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Divisibility Rules Worksheet

Vedic maths trick 13: Divisibility tests · Set 505 · 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 1119 divisible by 4?
  2. 2.Is 30744 divisible by 12?
  3. 3.Is 32886 divisible by 18?
  4. 4.Is 115038 divisible by 18?
  5. 5.Is 90036 divisible by 17?
  6. 6.Is 1821 divisible by 15?
  7. 7.Is 81374 divisible by 15?
  8. 8.Is 23769 divisible by 24?
  9. 9.Is 19198 divisible by 19?
  10. 10.Is 734 divisible by 7?
  11. 11.Is 16283 divisible by 10?
  12. 12.Is 58447 divisible by 19?
  13. 13.Is 16310 divisible by 3?
  14. 14.Is 6928 divisible by 6?
  15. 15.Is 21176 divisible by 4?
  16. 16.Is 31564 divisible by 5?
  17. 17.Is 50790 divisible by 15?
  18. 18.Is 73466 divisible by 13?
  19. 19.Is 12713 divisible by 2?
  20. 20.Is 9362 divisible by 30?
  21. 21.Is 9048 divisible by 4?
  22. 22.Is 22867 divisible by 23?
  23. 23.Is 16347 divisible by 8?
  24. 24.Is 99962 divisible by 18?
  25. 25.Is 93409 divisible by 29?
  26. 26.Is 390 divisible by 18?
  27. 27.Is 66572 divisible by 11?
  28. 28.Is 3357 divisible by 9?
  29. 29.Is 23478 divisible by 5?
  30. 30.Is 7139 divisible by 4?
  31. 31.Is 48708 divisible by 8?
  32. 32.Is 5152 divisible by 23?
  33. 33.Is 27852 divisible by 11?
  34. 34.Is 11975 divisible by 9?
  35. 35.Is 1285 divisible by 15?
  36. 36.Is 104978 divisible by 15?
  37. 37.Is 61116 divisible by 11?
  38. 38.Is 15580 divisible by 10?
  39. 39.Is 25805 divisible by 5?
  40. 40.Is 11265 divisible by 10?

Answer key

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

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