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Divisibility Rules Worksheet

Vedic maths trick 13: Divisibility tests · Set 845 · 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 11886 divisible by 19?
  2. 2.Is 56763 divisible by 9?
  3. 3.Is 35128 divisible by 7?
  4. 4.Is 125045 divisible by 19?
  5. 5.Is 114444 divisible by 24?
  6. 6.Is 13589 divisible by 2?
  7. 7.Is 9080 divisible by 5?
  8. 8.Is 7790 divisible by 5?
  9. 9.Is 24515 divisible by 17?
  10. 10.Is 11918 divisible by 2?
  11. 11.Is 39008 divisible by 8?
  12. 12.Is 69912 divisible by 12?
  13. 13.Is 9897 divisible by 17?
  14. 14.Is 75120 divisible by 15?
  15. 15.Is 121868 divisible by 30?
  16. 16.Is 35352 divisible by 9?
  17. 17.Is 8738 divisible by 6?
  18. 18.Is 8902 divisible by 3?
  19. 19.Is 1966 divisible by 10?
  20. 20.Is 9827 divisible by 18?
  21. 21.Is 101361 divisible by 23?
  22. 22.Is 18180 divisible by 15?
  23. 23.Is 4928 divisible by 11?
  24. 24.Is 79530 divisible by 15?
  25. 25.Is 33403 divisible by 23?
  26. 26.Is 134684 divisible by 20?
  27. 27.Is 169062 divisible by 29?
  28. 28.Is 79006 divisible by 20?
  29. 29.Is 119018 divisible by 23?
  30. 30.Is 40516 divisible by 7?
  31. 31.Is 138069 divisible by 29?
  32. 32.Is 76648 divisible by 29?
  33. 33.Is 3579 divisible by 2?
  34. 34.Is 108840 divisible by 24?
  35. 35.Is 27640 divisible by 4?
  36. 36.Is 6140 divisible by 3?
  37. 37.Is 64856 divisible by 11?
  38. 38.Is 107760 divisible by 20?
  39. 39.Is 4561 divisible by 2?
  40. 40.Is 49995 divisible by 15?

Answer key

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

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