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Divisibility Rules Worksheet

Vedic maths trick 13: Divisibility tests · Set 391 · 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 25583 divisible by 17?
  2. 2.Is 1179 divisible by 3?
  3. 3.Is 5775 divisible by 3?
  4. 4.Is 41922 divisible by 11?
  5. 5.Is 137771 divisible by 30?
  6. 6.Is 134389 divisible by 23?
  7. 7.Is 68320 divisible by 20?
  8. 8.Is 2880 divisible by 24?
  9. 9.Is 32937 divisible by 7?
  10. 10.Is 74584 divisible by 12?
  11. 11.Is 1330 divisible by 19?
  12. 12.Is 5863 divisible by 11?
  13. 13.Is 33748 divisible by 11?
  14. 14.Is 67505 divisible by 12?
  15. 15.Is 29328 divisible by 6?
  16. 16.Is 11188 divisible by 3?
  17. 17.Is 7125 divisible by 5?
  18. 18.Is 4172 divisible by 2?
  19. 19.Is 159744 divisible by 24?
  20. 20.Is 16143 divisible by 8?
  21. 21.Is 43617 divisible by 7?
  22. 22.Is 10604 divisible by 15?
  23. 23.Is 32966 divisible by 11?
  24. 24.Is 71136 divisible by 13?
  25. 25.Is 12859 divisible by 3?
  26. 26.Is 42328 divisible by 11?
  27. 27.Is 53677 divisible by 13?
  28. 28.Is 17840 divisible by 20?
  29. 29.Is 178003 divisible by 29?
  30. 30.Is 12018 divisible by 6?
  31. 31.Is 10407 divisible by 3?
  32. 32.Is 90195 divisible by 24?
  33. 33.Is 43588 divisible by 23?
  34. 34.Is 139710 divisible by 30?
  35. 35.Is 27340 divisible by 7?
  36. 36.Is 842 divisible by 3?
  37. 37.Is 42968 divisible by 9?
  38. 38.Is 1521 divisible by 12?
  39. 39.Is 48867 divisible by 20?
  40. 40.Is 101072 divisible by 17?

Answer key

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

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