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Divisibility Rules Worksheet

Vedic maths trick 13: Divisibility tests · Set 89 · 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 8625 divisible by 7?
  2. 2.Is 21645 divisible by 4?
  3. 3.Is 103755 divisible by 15?
  4. 4.Is 5992 divisible by 12?
  5. 5.Is 4401 divisible by 4?
  6. 6.Is 7117 divisible by 11?
  7. 7.Is 97020 divisible by 20?
  8. 8.Is 125234 divisible by 18?
  9. 9.Is 8724 divisible by 2?
  10. 10.Is 46010 divisible by 12?
  11. 11.Is 64566 divisible by 17?
  12. 12.Is 63780 divisible by 10?
  13. 13.Is 18469 divisible by 3?
  14. 14.Is 38504 divisible by 6?
  15. 15.Is 27516 divisible by 19?
  16. 16.Is 5630 divisible by 5?
  17. 17.Is 56603 divisible by 15?
  18. 18.Is 8390 divisible by 2?
  19. 19.Is 52670 divisible by 23?
  20. 20.Is 58820 divisible by 10?
  21. 21.Is 73296 divisible by 24?
  22. 22.Is 42848 divisible by 13?
  23. 23.Is 15441 divisible by 30?
  24. 24.Is 1514 divisible by 2?
  25. 25.Is 17465 divisible by 5?
  26. 26.Is 4858 divisible by 6?
  27. 27.Is 36693 divisible by 6?
  28. 28.Is 9448 divisible by 7?
  29. 29.Is 7282 divisible by 13?
  30. 30.Is 69715 divisible by 15?
  31. 31.Is 86800 divisible by 18?
  32. 32.Is 29196 divisible by 24?
  33. 33.Is 139084 divisible by 30?
  34. 34.Is 36652 divisible by 7?
  35. 35.Is 46312 divisible by 23?
  36. 36.Is 31590 divisible by 5?
  37. 37.Is 414 divisible by 2?
  38. 38.Is 85442 divisible by 23?
  39. 39.Is 38820 divisible by 20?
  40. 40.Is 18891 divisible by 3?

Answer key

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

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