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Divisibility Rules Worksheet

Vedic maths trick 13: Divisibility tests · Set 422 · 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 13190 divisible by 23?
  2. 2.Is 146234 divisible by 23?
  3. 3.Is 87652 divisible by 17?
  4. 4.Is 61116 divisible by 18?
  5. 5.Is 124177 divisible by 23?
  6. 6.Is 28281 divisible by 10?
  7. 7.Is 11250 divisible by 6?
  8. 8.Is 94250 divisible by 20?
  9. 9.Is 34340 divisible by 8?
  10. 10.Is 15921 divisible by 9?
  11. 11.Is 102423 divisible by 15?
  12. 12.Is 32148 divisible by 15?
  13. 13.Is 125120 divisible by 23?
  14. 14.Is 11598 divisible by 8?
  15. 15.Is 4200 divisible by 8?
  16. 16.Is 13011 divisible by 4?
  17. 17.Is 17155 divisible by 5?
  18. 18.Is 4536 divisible by 2?
  19. 19.Is 11664 divisible by 2?
  20. 20.Is 55063 divisible by 17?
  21. 21.Is 16213 divisible by 3?
  22. 22.Is 11815 divisible by 2?
  23. 23.Is 85531 divisible by 13?
  24. 24.Is 47977 divisible by 18?
  25. 25.Is 97812 divisible by 19?
  26. 26.Is 16690 divisible by 5?
  27. 27.Is 164493 divisible by 29?
  28. 28.Is 20686 divisible by 3?
  29. 29.Is 7130 divisible by 4?
  30. 30.Is 32397 divisible by 6?
  31. 31.Is 4264 divisible by 3?
  32. 32.Is 14384 divisible by 17?
  33. 33.Is 78949 divisible by 13?
  34. 34.Is 26736 divisible by 10?
  35. 35.Is 35344 divisible by 8?
  36. 36.Is 16711 divisible by 20?
  37. 37.Is 91437 divisible by 18?
  38. 38.Is 2241 divisible by 3?
  39. 39.Is 25417 divisible by 7?
  40. 40.Is 48838 divisible by 18?

Answer key

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

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