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Divisibility Rules Worksheet

Vedic maths trick 13: Divisibility tests · Set 485 · 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 44326 divisible by 19?
  2. 2.Is 81989 divisible by 13?
  3. 3.Is 6727 divisible by 2?
  4. 4.Is 27961 divisible by 6?
  5. 5.Is 122100 divisible by 24?
  6. 6.Is 18517 divisible by 11?
  7. 7.Is 20033 divisible by 10?
  8. 8.Is 19494 divisible by 3?
  9. 9.Is 181436 divisible by 30?
  10. 10.Is 74195 divisible by 29?
  11. 11.Is 70667 divisible by 30?
  12. 12.Is 6494 divisible by 4?
  13. 13.Is 45200 divisible by 7?
  14. 14.Is 49200 divisible by 9?
  15. 15.Is 56212 divisible by 15?
  16. 16.Is 14252 divisible by 7?
  17. 17.Is 116608 divisible by 17?
  18. 18.Is 77168 divisible by 20?
  19. 19.Is 21048 divisible by 12?
  20. 20.Is 5538 divisible by 3?
  21. 21.Is 47035 divisible by 10?
  22. 22.Is 13048 divisible by 4?
  23. 23.Is 52553 divisible by 30?
  24. 24.Is 26841 divisible by 4?
  25. 25.Is 37201 divisible by 10?
  26. 26.Is 27164 divisible by 18?
  27. 27.Is 10686 divisible by 6?
  28. 28.Is 79110 divisible by 15?
  29. 29.Is 12165 divisible by 2?
  30. 30.Is 49155 divisible by 29?
  31. 31.Is 11513 divisible by 15?
  32. 32.Is 1470 divisible by 5?
  33. 33.Is 72160 divisible by 11?
  34. 34.Is 119976 divisible by 24?
  35. 35.Is 7918 divisible by 6?
  36. 36.Is 34353 divisible by 9?
  37. 37.Is 6420 divisible by 9?
  38. 38.Is 9015 divisible by 5?
  39. 39.Is 2005 divisible by 6?
  40. 40.Is 5041 divisible by 19?

Answer key

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

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