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Divisibility Rules Worksheet

Vedic maths trick 13: Divisibility tests · Set 924 · 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 17700 divisible by 3?
  2. 2.Is 34736 divisible by 13?
  3. 3.Is 30407 divisible by 11?
  4. 4.Is 28712 divisible by 9?
  5. 5.Is 40689 divisible by 11?
  6. 6.Is 37277 divisible by 6?
  7. 7.Is 93406 divisible by 17?
  8. 8.Is 1024 divisible by 2?
  9. 9.Is 3690 divisible by 2?
  10. 10.Is 15930 divisible by 5?
  11. 11.Is 33020 divisible by 20?
  12. 12.Is 8899 divisible by 11?
  13. 13.Is 25836 divisible by 12?
  14. 14.Is 22104 divisible by 18?
  15. 15.Is 57696 divisible by 12?
  16. 16.Is 46093 divisible by 7?
  17. 17.Is 28133 divisible by 7?
  18. 18.Is 12254 divisible by 3?
  19. 19.Is 20952 divisible by 8?
  20. 20.Is 50024 divisible by 11?
  21. 21.Is 32450 divisible by 10?
  22. 22.Is 600 divisible by 30?
  23. 23.Is 35946 divisible by 6?
  24. 24.Is 12135 divisible by 3?
  25. 25.Is 6717 divisible by 3?
  26. 26.Is 182697 divisible by 29?
  27. 27.Is 18581 divisible by 17?
  28. 28.Is 11558 divisible by 2?
  29. 29.Is 135151 divisible by 29?
  30. 30.Is 448 divisible by 7?
  31. 31.Is 48673 divisible by 12?
  32. 32.Is 36511 divisible by 29?
  33. 33.Is 64278 divisible by 18?
  34. 34.Is 22385 divisible by 11?
  35. 35.Is 10145 divisible by 3?
  36. 36.Is 135068 divisible by 24?
  37. 37.Is 50165 divisible by 30?
  38. 38.Is 163859 divisible by 30?
  39. 39.Is 98660 divisible by 20?
  40. 40.Is 21375 divisible by 20?

Answer key

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

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