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Divisibility Rules Worksheet

Vedic maths trick 13: Divisibility tests · Set 575 · 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 57432 divisible by 24?
  2. 2.Is 6990 divisible by 5?
  3. 3.Is 20112 divisible by 4?
  4. 4.Is 65831 divisible by 11?
  5. 5.Is 75532 divisible by 23?
  6. 6.Is 3154 divisible by 2?
  7. 7.Is 108205 divisible by 19?
  8. 8.Is 125918 divisible by 29?
  9. 9.Is 45370 divisible by 8?
  10. 10.Is 41207 divisible by 15?
  11. 11.Is 172955 divisible by 30?
  12. 12.Is 67528 divisible by 23?
  13. 13.Is 12708 divisible by 2?
  14. 14.Is 64797 divisible by 23?
  15. 15.Is 14887 divisible by 3?
  16. 16.Is 80600 divisible by 20?
  17. 17.Is 49384 divisible by 8?
  18. 18.Is 19232 divisible by 4?
  19. 19.Is 67750 divisible by 10?
  20. 20.Is 10087 divisible by 3?
  21. 21.Is 39960 divisible by 18?
  22. 22.Is 69982 divisible by 11?
  23. 23.Is 2141 divisible by 6?
  24. 24.Is 156210 divisible by 30?
  25. 25.Is 6623 divisible by 6?
  26. 26.Is 11417 divisible by 8?
  27. 27.Is 2892 divisible by 15?
  28. 28.Is 37238 divisible by 18?
  29. 29.Is 16455 divisible by 5?
  30. 30.Is 18788 divisible by 4?
  31. 31.Is 312 divisible by 10?
  32. 32.Is 18328 divisible by 6?
  33. 33.Is 137540 divisible by 23?
  34. 34.Is 19198 divisible by 10?
  35. 35.Is 36012 divisible by 11?
  36. 36.Is 1423 divisible by 5?
  37. 37.Is 6629 divisible by 4?
  38. 38.Is 60203 divisible by 11?
  39. 39.Is 68055 divisible by 15?
  40. 40.Is 77510 divisible by 23?

Answer key

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

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