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Divisibility Rules Worksheet

Vedic maths trick 13: Divisibility tests · Set 69 · 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 10755 divisible by 5?
  2. 2.Is 149736 divisible by 30?
  3. 3.Is 36120 divisible by 20?
  4. 4.Is 55420 divisible by 17?
  5. 5.Is 19684 divisible by 7?
  6. 6.Is 71427 divisible by 29?
  7. 7.Is 3900 divisible by 15?
  8. 8.Is 87783 divisible by 29?
  9. 9.Is 3706 divisible by 5?
  10. 10.Is 34450 divisible by 10?
  11. 11.Is 21581 divisible by 5?
  12. 12.Is 74940 divisible by 12?
  13. 13.Is 50380 divisible by 9?
  14. 14.Is 28440 divisible by 5?
  15. 15.Is 47220 divisible by 12?
  16. 16.Is 15844 divisible by 3?
  17. 17.Is 6157 divisible by 2?
  18. 18.Is 15626 divisible by 9?
  19. 19.Is 73174 divisible by 11?
  20. 20.Is 95904 divisible by 17?
  21. 21.Is 56306 divisible by 11?
  22. 22.Is 10190 divisible by 5?
  23. 23.Is 6368 divisible by 8?
  24. 24.Is 13121 divisible by 2?
  25. 25.Is 8329 divisible by 7?
  26. 26.Is 7299 divisible by 7?
  27. 27.Is 40898 divisible by 17?
  28. 28.Is 19759 divisible by 20?
  29. 29.Is 52753 divisible by 8?
  30. 30.Is 46784 divisible by 19?
  31. 31.Is 55311 divisible by 30?
  32. 32.Is 24098 divisible by 4?
  33. 33.Is 27972 divisible by 10?
  34. 34.Is 12056 divisible by 2?
  35. 35.Is 4785 divisible by 29?
  36. 36.Is 33678 divisible by 6?
  37. 37.Is 1128 divisible by 2?
  38. 38.Is 32362 divisible by 11?
  39. 39.Is 108629 divisible by 23?
  40. 40.Is 72954 divisible by 19?

Answer key

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

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