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Divisibility Rules Worksheet

Vedic maths trick 13: Divisibility tests · Set 709 · 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 42057 divisible by 9?
  2. 2.Is 24264 divisible by 7?
  3. 3.Is 12194 divisible by 13?
  4. 4.Is 768 divisible by 4?
  5. 5.Is 45191 divisible by 11?
  6. 6.Is 23928 divisible by 6?
  7. 7.Is 8830 divisible by 7?
  8. 8.Is 10812 divisible by 8?
  9. 9.Is 22209 divisible by 11?
  10. 10.Is 28656 divisible by 6?
  11. 11.Is 8178 divisible by 29?
  12. 12.Is 23064 divisible by 4?
  13. 13.Is 29860 divisible by 6?
  14. 14.Is 5432 divisible by 23?
  15. 15.Is 107640 divisible by 18?
  16. 16.Is 34766 divisible by 6?
  17. 17.Is 160131 divisible by 23?
  18. 18.Is 10082 divisible by 2?
  19. 19.Is 71621 divisible by 13?
  20. 20.Is 3427 divisible by 23?
  21. 21.Is 97622 divisible by 19?
  22. 22.Is 39412 divisible by 10?
  23. 23.Is 3943 divisible by 2?
  24. 24.Is 21616 divisible by 7?
  25. 25.Is 69118 divisible by 15?
  26. 26.Is 10641 divisible by 3?
  27. 27.Is 73458 divisible by 18?
  28. 28.Is 13494 divisible by 7?
  29. 29.Is 71114 divisible by 17?
  30. 30.Is 61897 divisible by 11?
  31. 31.Is 22456 divisible by 8?
  32. 32.Is 11570 divisible by 10?
  33. 33.Is 6791 divisible by 2?
  34. 34.Is 2384 divisible by 5?
  35. 35.Is 40985 divisible by 7?
  36. 36.Is 56444 divisible by 19?
  37. 37.Is 6920 divisible by 10?
  38. 38.Is 36830 divisible by 29?
  39. 39.Is 55745 divisible by 10?
  40. 40.Is 49699 divisible by 13?

Answer key

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

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