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Divisibility Rules Worksheet

Vedic maths trick 13: Divisibility tests · Set 259 · 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 49197 divisible by 23?
  2. 2.Is 36428 divisible by 19?
  3. 3.Is 13208 divisible by 2?
  4. 4.Is 180177 divisible by 29?
  5. 5.Is 10400 divisible by 4?
  6. 6.Is 633 divisible by 2?
  7. 7.Is 52234 divisible by 13?
  8. 8.Is 49082 divisible by 23?
  9. 9.Is 61313 divisible by 30?
  10. 10.Is 52854 divisible by 23?
  11. 11.Is 17860 divisible by 19?
  12. 12.Is 73864 divisible by 11?
  13. 13.Is 93258 divisible by 18?
  14. 14.Is 15130 divisible by 13?
  15. 15.Is 6080 divisible by 23?
  16. 16.Is 18046 divisible by 4?
  17. 17.Is 4768 divisible by 19?
  18. 18.Is 59100 divisible by 15?
  19. 19.Is 38964 divisible by 12?
  20. 20.Is 24923 divisible by 7?
  21. 21.Is 136152 divisible by 24?
  22. 22.Is 4702 divisible by 30?
  23. 23.Is 40845 divisible by 7?
  24. 24.Is 39750 divisible by 10?
  25. 25.Is 33939 divisible by 20?
  26. 26.Is 3734 divisible by 3?
  27. 27.Is 32855 divisible by 5?
  28. 28.Is 10538 divisible by 3?
  29. 29.Is 574 divisible by 9?
  30. 30.Is 137808 divisible by 24?
  31. 31.Is 21375 divisible by 29?
  32. 32.Is 18176 divisible by 4?
  33. 33.Is 21918 divisible by 13?
  34. 34.Is 49294 divisible by 8?
  35. 35.Is 89245 divisible by 24?
  36. 36.Is 42946 divisible by 20?
  37. 37.Is 4547 divisible by 9?
  38. 38.Is 51586 divisible by 12?
  39. 39.Is 855 divisible by 19?
  40. 40.Is 13086 divisible by 6?

Answer key

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

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