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Divisibility Rules Worksheet

Vedic maths trick 13: Divisibility tests · Set 797 · 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 30169 divisible by 13?
  2. 2.Is 146224 divisible by 30?
  3. 3.Is 13258 divisible by 6?
  4. 4.Is 42077 divisible by 12?
  5. 5.Is 32235 divisible by 7?
  6. 6.Is 30599 divisible by 6?
  7. 7.Is 33102 divisible by 9?
  8. 8.Is 22433 divisible by 10?
  9. 9.Is 28899 divisible by 7?
  10. 10.Is 8943 divisible by 3?
  11. 11.Is 105726 divisible by 24?
  12. 12.Is 21760 divisible by 5?
  13. 13.Is 29070 divisible by 9?
  14. 14.Is 31619 divisible by 24?
  15. 15.Is 57687 divisible by 29?
  16. 16.Is 12040 divisible by 7?
  17. 17.Is 94494 divisible by 18?
  18. 18.Is 20570 divisible by 10?
  19. 19.Is 74520 divisible by 11?
  20. 20.Is 23338 divisible by 5?
  21. 21.Is 40352 divisible by 8?
  22. 22.Is 23630 divisible by 4?
  23. 23.Is 6049 divisible by 7?
  24. 24.Is 9413 divisible by 3?
  25. 25.Is 89424 divisible by 23?
  26. 26.Is 15576 divisible by 11?
  27. 27.Is 6648 divisible by 8?
  28. 28.Is 45585 divisible by 9?
  29. 29.Is 18485 divisible by 29?
  30. 30.Is 44498 divisible by 8?
  31. 31.Is 48384 divisible by 24?
  32. 32.Is 6381 divisible by 6?
  33. 33.Is 55267 divisible by 9?
  34. 34.Is 20931 divisible by 30?
  35. 35.Is 7370 divisible by 4?
  36. 36.Is 41126 divisible by 10?
  37. 37.Is 53340 divisible by 9?
  38. 38.Is 12840 divisible by 6?
  39. 39.Is 85964 divisible by 24?
  40. 40.Is 146430 divisible by 29?

Answer key

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

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