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Divisibility Rules Worksheet

Vedic maths trick 13: Divisibility tests · Set 463 · 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 25140 divisible by 10?
  2. 2.Is 7588 divisible by 5?
  3. 3.Is 66218 divisible by 12?
  4. 4.Is 89155 divisible by 19?
  5. 5.Is 15147 divisible by 15?
  6. 6.Is 31440 divisible by 5?
  7. 7.Is 103277 divisible by 17?
  8. 8.Is 17704 divisible by 7?
  9. 9.Is 84200 divisible by 13?
  10. 10.Is 164382 divisible by 30?
  11. 11.Is 21593 divisible by 4?
  12. 12.Is 5909 divisible by 7?
  13. 13.Is 8844 divisible by 6?
  14. 14.Is 6874 divisible by 17?
  15. 15.Is 61035 divisible by 15?
  16. 16.Is 13208 divisible by 13?
  17. 17.Is 8808 divisible by 4?
  18. 18.Is 64061 divisible by 29?
  19. 19.Is 14408 divisible by 5?
  20. 20.Is 13229 divisible by 4?
  21. 21.Is 25722 divisible by 18?
  22. 22.Is 35693 divisible by 7?
  23. 23.Is 1170 divisible by 4?
  24. 24.Is 13132 divisible by 2?
  25. 25.Is 105031 divisible by 29?
  26. 26.Is 3270 divisible by 5?
  27. 27.Is 5053 divisible by 18?
  28. 28.Is 3051 divisible by 10?
  29. 29.Is 7455 divisible by 6?
  30. 30.Is 82505 divisible by 29?
  31. 31.Is 12747 divisible by 3?
  32. 32.Is 155370 divisible by 30?
  33. 33.Is 28800 divisible by 8?
  34. 34.Is 22372 divisible by 7?
  35. 35.Is 49097 divisible by 29?
  36. 36.Is 428 divisible by 6?
  37. 37.Is 48173 divisible by 8?
  38. 38.Is 11310 divisible by 2?
  39. 39.Is 55180 divisible by 9?
  40. 40.Is 29689 divisible by 12?

Answer key

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

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