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Divisibility Rules Worksheet

Vedic maths trick 13: Divisibility tests · Set 234 · 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 11934 divisible by 17?
  2. 2.Is 62376 divisible by 12?
  3. 3.Is 107179 divisible by 19?
  4. 4.Is 12537 divisible by 29?
  5. 5.Is 150570 divisible by 23?
  6. 6.Is 29738 divisible by 10?
  7. 7.Is 146715 divisible by 29?
  8. 8.Is 5736 divisible by 6?
  9. 9.Is 17250 divisible by 6?
  10. 10.Is 569 divisible by 2?
  11. 11.Is 90898 divisible by 20?
  12. 12.Is 3238 divisible by 3?
  13. 13.Is 16968 divisible by 12?
  14. 14.Is 121938 divisible by 30?
  15. 15.Is 22253 divisible by 7?
  16. 16.Is 60078 divisible by 17?
  17. 17.Is 5683 divisible by 3?
  18. 18.Is 468 divisible by 6?
  19. 19.Is 60889 divisible by 9?
  20. 20.Is 18158 divisible by 3?
  21. 21.Is 94893 divisible by 15?
  22. 22.Is 35553 divisible by 8?
  23. 23.Is 99853 divisible by 15?
  24. 24.Is 53880 divisible by 30?
  25. 25.Is 11490 divisible by 6?
  26. 26.Is 88322 divisible by 15?
  27. 27.Is 3158 divisible by 2?
  28. 28.Is 11949 divisible by 7?
  29. 29.Is 3525 divisible by 3?
  30. 30.Is 1308 divisible by 3?
  31. 31.Is 68817 divisible by 12?
  32. 32.Is 11557 divisible by 7?
  33. 33.Is 64008 divisible by 24?
  34. 34.Is 77515 divisible by 12?
  35. 35.Is 16085 divisible by 20?
  36. 36.Is 27928 divisible by 12?
  37. 37.Is 26848 divisible by 8?
  38. 38.Is 11962 divisible by 5?
  39. 39.Is 25185 divisible by 5?
  40. 40.Is 3071 divisible by 2?

Answer key

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

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