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Divisibility Rules Worksheet

Vedic maths trick 13: Divisibility tests · Set 537 · 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 9124 divisible by 3?
  2. 2.Is 13864 divisible by 4?
  3. 3.Is 11711 divisible by 2?
  4. 4.Is 19721 divisible by 4?
  5. 5.Is 8414 divisible by 7?
  6. 6.Is 5597 divisible by 2?
  7. 7.Is 9011 divisible by 11?
  8. 8.Is 184050 divisible by 30?
  9. 9.Is 8897 divisible by 7?
  10. 10.Is 14340 divisible by 30?
  11. 11.Is 58018 divisible by 9?
  12. 12.Is 82916 divisible by 19?
  13. 13.Is 46650 divisible by 15?
  14. 14.Is 20361 divisible by 3?
  15. 15.Is 84156 divisible by 20?
  16. 16.Is 32962 divisible by 8?
  17. 17.Is 1188 divisible by 2?
  18. 18.Is 108474 divisible by 23?
  19. 19.Is 39160 divisible by 8?
  20. 20.Is 105248 divisible by 23?
  21. 21.Is 175331 divisible by 30?
  22. 22.Is 138700 divisible by 29?
  23. 23.Is 51415 divisible by 10?
  24. 24.Is 51070 divisible by 20?
  25. 25.Is 6185 divisible by 7?
  26. 26.Is 14084 divisible by 7?
  27. 27.Is 46870 divisible by 10?
  28. 28.Is 37100 divisible by 10?
  29. 29.Is 36984 divisible by 23?
  30. 30.Is 99330 divisible by 30?
  31. 31.Is 75922 divisible by 17?
  32. 32.Is 5580 divisible by 20?
  33. 33.Is 6561 divisible by 3?
  34. 34.Is 36195 divisible by 15?
  35. 35.Is 31627 divisible by 17?
  36. 36.Is 59849 divisible by 13?
  37. 37.Is 110300 divisible by 19?
  38. 38.Is 38001 divisible by 7?
  39. 39.Is 10723 divisible by 3?
  40. 40.Is 44343 divisible by 17?

Answer key

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

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