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Divisibility Rules Worksheet

Vedic maths trick 13: Divisibility tests · Set 388 · 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 1829 divisible by 3?
  2. 2.Is 21836 divisible by 24?
  3. 3.Is 180150 divisible by 30?
  4. 4.Is 30544 divisible by 19?
  5. 5.Is 27677 divisible by 13?
  6. 6.Is 36274 divisible by 10?
  7. 7.Is 9360 divisible by 9?
  8. 8.Is 59758 divisible by 9?
  9. 9.Is 107634 divisible by 29?
  10. 10.Is 56238 divisible by 20?
  11. 11.Is 104493 divisible by 17?
  12. 12.Is 14099 divisible by 6?
  13. 13.Is 81906 divisible by 24?
  14. 14.Is 33525 divisible by 15?
  15. 15.Is 16875 divisible by 4?
  16. 16.Is 111480 divisible by 17?
  17. 17.Is 4088 divisible by 7?
  18. 18.Is 61984 divisible by 12?
  19. 19.Is 6998 divisible by 10?
  20. 20.Is 64067 divisible by 24?
  21. 21.Is 71566 divisible by 11?
  22. 22.Is 18813 divisible by 11?
  23. 23.Is 7282 divisible by 11?
  24. 24.Is 11327 divisible by 3?
  25. 25.Is 33887 divisible by 10?
  26. 26.Is 74011 divisible by 23?
  27. 27.Is 14273 divisible by 7?
  28. 28.Is 94333 divisible by 17?
  29. 29.Is 8442 divisible by 3?
  30. 30.Is 43645 divisible by 15?
  31. 31.Is 38500 divisible by 11?
  32. 32.Is 43008 divisible by 8?
  33. 33.Is 28512 divisible by 6?
  34. 34.Is 35595 divisible by 9?
  35. 35.Is 3040 divisible by 4?
  36. 36.Is 118260 divisible by 20?
  37. 37.Is 211 divisible by 3?
  38. 38.Is 48162 divisible by 23?
  39. 39.Is 112482 divisible by 18?
  40. 40.Is 4089 divisible by 23?

Answer key

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

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