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Divisibility Rules Worksheet

Vedic maths trick 13: Divisibility tests · Set 494 · 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 28568 divisible by 19?
  2. 2.Is 34727 divisible by 7?
  3. 3.Is 58861 divisible by 12?
  4. 4.Is 40320 divisible by 6?
  5. 5.Is 14448 divisible by 6?
  6. 6.Is 1728 divisible by 2?
  7. 7.Is 45852 divisible by 17?
  8. 8.Is 57532 divisible by 19?
  9. 9.Is 107029 divisible by 30?
  10. 10.Is 32766 divisible by 9?
  11. 11.Is 483 divisible by 2?
  12. 12.Is 37715 divisible by 19?
  13. 13.Is 115420 divisible by 20?
  14. 14.Is 38077 divisible by 6?
  15. 15.Is 5275 divisible by 7?
  16. 16.Is 53131 divisible by 13?
  17. 17.Is 3690 divisible by 18?
  18. 18.Is 159120 divisible by 24?
  19. 19.Is 13653 divisible by 2?
  20. 20.Is 14250 divisible by 3?
  21. 21.Is 19432 divisible by 3?
  22. 22.Is 85103 divisible by 20?
  23. 23.Is 71841 divisible by 13?
  24. 24.Is 81458 divisible by 13?
  25. 25.Is 2981 divisible by 24?
  26. 26.Is 115362 divisible by 17?
  27. 27.Is 57712 divisible by 20?
  28. 28.Is 63307 divisible by 29?
  29. 29.Is 41923 divisible by 20?
  30. 30.Is 1393 divisible by 5?
  31. 31.Is 26739 divisible by 4?
  32. 32.Is 4934 divisible by 13?
  33. 33.Is 143664 divisible by 24?
  34. 34.Is 37912 divisible by 10?
  35. 35.Is 205334 divisible by 30?
  36. 36.Is 9108 divisible by 4?
  37. 37.Is 83256 divisible by 12?
  38. 38.Is 58223 divisible by 30?
  39. 39.Is 12158 divisible by 8?
  40. 40.Is 7644 divisible by 4?

Answer key

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

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