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Divisibility Rules Worksheet

Vedic maths trick 13: Divisibility tests · Set 7 · 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 60514 divisible by 19?
  2. 2.Is 92358 divisible by 30?
  3. 3.Is 4396 divisible by 12?
  4. 4.Is 57160 divisible by 20?
  5. 5.Is 16993 divisible by 19?
  6. 6.Is 17487 divisible by 4?
  7. 7.Is 6885 divisible by 5?
  8. 8.Is 13269 divisible by 4?
  9. 9.Is 48930 divisible by 7?
  10. 10.Is 142071 divisible by 29?
  11. 11.Is 30585 divisible by 7?
  12. 12.Is 29009 divisible by 19?
  13. 13.Is 5901 divisible by 2?
  14. 14.Is 11436 divisible by 6?
  15. 15.Is 109786 divisible by 17?
  16. 16.Is 43170 divisible by 30?
  17. 17.Is 65402 divisible by 11?
  18. 18.Is 2346 divisible by 6?
  19. 19.Is 26723 divisible by 4?
  20. 20.Is 59448 divisible by 24?
  21. 21.Is 133776 divisible by 23?
  22. 22.Is 30339 divisible by 9?
  23. 23.Is 61558 divisible by 20?
  24. 24.Is 45218 divisible by 23?
  25. 25.Is 118133 divisible by 17?
  26. 26.Is 22003 divisible by 6?
  27. 27.Is 77940 divisible by 30?
  28. 28.Is 100875 divisible by 15?
  29. 29.Is 24893 divisible by 7?
  30. 30.Is 14168 divisible by 7?
  31. 31.Is 61841 divisible by 9?
  32. 32.Is 47805 divisible by 8?
  33. 33.Is 19728 divisible by 3?
  34. 34.Is 3650 divisible by 4?
  35. 35.Is 30973 divisible by 9?
  36. 36.Is 11709 divisible by 7?
  37. 37.Is 3564 divisible by 18?
  38. 38.Is 265 divisible by 3?
  39. 39.Is 116946 divisible by 18?
  40. 40.Is 19812 divisible by 6?

Answer key

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

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