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Divisibility Rules Worksheet

Vedic maths trick 13: Divisibility tests · Set 828 · 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 7284 divisible by 6?
  2. 2.Is 74370 divisible by 15?
  3. 3.Is 33315 divisible by 8?
  4. 4.Is 7490 divisible by 15?
  5. 5.Is 27984 divisible by 7?
  6. 6.Is 31066 divisible by 9?
  7. 7.Is 4686 divisible by 10?
  8. 8.Is 69732 divisible by 13?
  9. 9.Is 3656 divisible by 8?
  10. 10.Is 4370 divisible by 5?
  11. 11.Is 35430 divisible by 30?
  12. 12.Is 149118 divisible by 29?
  13. 13.Is 52304 divisible by 8?
  14. 14.Is 1507 divisible by 4?
  15. 15.Is 115286 divisible by 18?
  16. 16.Is 33281 divisible by 29?
  17. 17.Is 22386 divisible by 19?
  18. 18.Is 70568 divisible by 13?
  19. 19.Is 58090 divisible by 12?
  20. 20.Is 84058 divisible by 13?
  21. 21.Is 4055 divisible by 4?
  22. 22.Is 76365 divisible by 20?
  23. 23.Is 72439 divisible by 18?
  24. 24.Is 7854 divisible by 7?
  25. 25.Is 11176 divisible by 2?
  26. 26.Is 196939 divisible by 29?
  27. 27.Is 13086 divisible by 9?
  28. 28.Is 131446 divisible by 23?
  29. 29.Is 109368 divisible by 18?
  30. 30.Is 14076 divisible by 3?
  31. 31.Is 115178 divisible by 19?
  32. 32.Is 74112 divisible by 12?
  33. 33.Is 22990 divisible by 5?
  34. 34.Is 133056 divisible by 24?
  35. 35.Is 77688 divisible by 24?
  36. 36.Is 23764 divisible by 8?
  37. 37.Is 21431 divisible by 5?
  38. 38.Is 15104 divisible by 15?
  39. 39.Is 61428 divisible by 19?
  40. 40.Is 55025 divisible by 30?

Answer key

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

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