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Divisibility Rules Worksheet

Vedic maths trick 13: Divisibility tests · Set 81 · 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 33530 divisible by 5?
  2. 2.Is 60075 divisible by 9?
  3. 3.Is 182133 divisible by 30?
  4. 4.Is 58350 divisible by 10?
  5. 5.Is 12616 divisible by 8?
  6. 6.Is 3609 divisible by 3?
  7. 7.Is 17695 divisible by 19?
  8. 8.Is 85663 divisible by 17?
  9. 9.Is 108851 divisible by 17?
  10. 10.Is 29337 divisible by 11?
  11. 11.Is 4823 divisible by 3?
  12. 12.Is 1839 divisible by 30?
  13. 13.Is 60344 divisible by 19?
  14. 14.Is 84413 divisible by 18?
  15. 15.Is 61932 divisible by 9?
  16. 16.Is 55220 divisible by 11?
  17. 17.Is 44856 divisible by 12?
  18. 18.Is 11372 divisible by 6?
  19. 19.Is 19308 divisible by 3?
  20. 20.Is 124453 divisible by 30?
  21. 21.Is 30700 divisible by 17?
  22. 22.Is 69686 divisible by 10?
  23. 23.Is 125480 divisible by 20?
  24. 24.Is 45457 divisible by 10?
  25. 25.Is 102707 divisible by 24?
  26. 26.Is 50314 divisible by 12?
  27. 27.Is 40618 divisible by 23?
  28. 28.Is 100192 divisible by 20?
  29. 29.Is 101452 divisible by 15?
  30. 30.Is 29943 divisible by 9?
  31. 31.Is 93066 divisible by 23?
  32. 32.Is 14877 divisible by 3?
  33. 33.Is 99772 divisible by 30?
  34. 34.Is 155914 divisible by 23?
  35. 35.Is 19935 divisible by 4?
  36. 36.Is 69080 divisible by 29?
  37. 37.Is 74054 divisible by 19?
  38. 38.Is 2064 divisible by 3?
  39. 39.Is 14303 divisible by 13?
  40. 40.Is 7196 divisible by 7?

Answer key

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

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