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Divisibility Rules Worksheet

Vedic maths trick 13: Divisibility tests · Set 172 · 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 13742 divisible by 13?
  2. 2.Is 2940 divisible by 15?
  3. 3.Is 23224 divisible by 20?
  4. 4.Is 25344 divisible by 8?
  5. 5.Is 96284 divisible by 29?
  6. 6.Is 72958 divisible by 11?
  7. 7.Is 38940 divisible by 9?
  8. 8.Is 110420 divisible by 20?
  9. 9.Is 61237 divisible by 11?
  10. 10.Is 10548 divisible by 6?
  11. 11.Is 47481 divisible by 18?
  12. 12.Is 70039 divisible by 12?
  13. 13.Is 19494 divisible by 19?
  14. 14.Is 11088 divisible by 24?
  15. 15.Is 6936 divisible by 4?
  16. 16.Is 94129 divisible by 17?
  17. 17.Is 11064 divisible by 3?
  18. 18.Is 24348 divisible by 12?
  19. 19.Is 35897 divisible by 6?
  20. 20.Is 80910 divisible by 15?
  21. 21.Is 7998 divisible by 30?
  22. 22.Is 70460 divisible by 15?
  23. 23.Is 11817 divisible by 7?
  24. 24.Is 5863 divisible by 3?
  25. 25.Is 17466 divisible by 3?
  26. 26.Is 105120 divisible by 23?
  27. 27.Is 4502 divisible by 12?
  28. 28.Is 13692 divisible by 12?
  29. 29.Is 32677 divisible by 13?
  30. 30.Is 1769 divisible by 3?
  31. 31.Is 141930 divisible by 30?
  32. 32.Is 38084 divisible by 7?
  33. 33.Is 188877 divisible by 29?
  34. 34.Is 101970 divisible by 30?
  35. 35.Is 56455 divisible by 20?
  36. 36.Is 1559 divisible by 2?
  37. 37.Is 5260 divisible by 10?
  38. 38.Is 85176 divisible by 24?
  39. 39.Is 3619 divisible by 5?
  40. 40.Is 2400 divisible by 2?

Answer key

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

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