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Divisibility Rules Worksheet

Vedic maths trick 13: Divisibility tests · Set 325 · 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 48312 divisible by 12?
  2. 2.Is 9952 divisible by 9?
  3. 3.Is 41980 divisible by 6?
  4. 4.Is 81472 divisible by 12?
  5. 5.Is 47212 divisible by 29?
  6. 6.Is 47623 divisible by 11?
  7. 7.Is 46601 divisible by 10?
  8. 8.Is 51870 divisible by 30?
  9. 9.Is 10345 divisible by 4?
  10. 10.Is 16920 divisible by 15?
  11. 11.Is 112890 divisible by 20?
  12. 12.Is 40856 divisible by 8?
  13. 13.Is 144840 divisible by 24?
  14. 14.Is 5247 divisible by 2?
  15. 15.Is 9951 divisible by 4?
  16. 16.Is 52442 divisible by 24?
  17. 17.Is 10430 divisible by 2?
  18. 18.Is 25632 divisible by 17?
  19. 19.Is 7065 divisible by 3?
  20. 20.Is 57699 divisible by 9?
  21. 21.Is 40035 divisible by 17?
  22. 22.Is 31105 divisible by 6?
  23. 23.Is 58715 divisible by 11?
  24. 24.Is 7824 divisible by 3?
  25. 25.Is 97092 divisible by 18?
  26. 26.Is 48970 divisible by 10?
  27. 27.Is 83034 divisible by 20?
  28. 28.Is 33719 divisible by 7?
  29. 29.Is 90873 divisible by 15?
  30. 30.Is 96900 divisible by 17?
  31. 31.Is 29587 divisible by 11?
  32. 32.Is 64157 divisible by 29?
  33. 33.Is 30147 divisible by 8?
  34. 34.Is 9961 divisible by 6?
  35. 35.Is 9008 divisible by 19?
  36. 36.Is 71580 divisible by 20?
  37. 37.Is 18615 divisible by 9?
  38. 38.Is 125457 divisible by 19?
  39. 39.Is 54002 divisible by 8?
  40. 40.Is 31743 divisible by 9?

Answer key

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

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