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Divisibility Rules Worksheet

Vedic maths trick 13: Divisibility tests · Set 766 · 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 1362 divisible by 6?
  2. 2.Is 11674 divisible by 2?
  3. 3.Is 35777 divisible by 19?
  4. 4.Is 25735 divisible by 24?
  5. 5.Is 57600 divisible by 20?
  6. 6.Is 21800 divisible by 4?
  7. 7.Is 32567 divisible by 5?
  8. 8.Is 1258 divisible by 2?
  9. 9.Is 28226 divisible by 10?
  10. 10.Is 56160 divisible by 12?
  11. 11.Is 21608 divisible by 4?
  12. 12.Is 60696 divisible by 10?
  13. 13.Is 113577 divisible by 17?
  14. 14.Is 20715 divisible by 10?
  15. 15.Is 56160 divisible by 10?
  16. 16.Is 118541 divisible by 17?
  17. 17.Is 17678 divisible by 3?
  18. 18.Is 3364 divisible by 8?
  19. 19.Is 111870 divisible by 30?
  20. 20.Is 74451 divisible by 13?
  21. 21.Is 57704 divisible by 10?
  22. 22.Is 77278 divisible by 24?
  23. 23.Is 132621 divisible by 24?
  24. 24.Is 22270 divisible by 5?
  25. 25.Is 56903 divisible by 12?
  26. 26.Is 1841 divisible by 2?
  27. 27.Is 5830 divisible by 11?
  28. 28.Is 1724 divisible by 4?
  29. 29.Is 93931 divisible by 29?
  30. 30.Is 51561 divisible by 17?
  31. 31.Is 5297 divisible by 7?
  32. 32.Is 22284 divisible by 11?
  33. 33.Is 41690 divisible by 10?
  34. 34.Is 58305 divisible by 15?
  35. 35.Is 38250 divisible by 18?
  36. 36.Is 21857 divisible by 10?
  37. 37.Is 10668 divisible by 4?
  38. 38.Is 118776 divisible by 24?
  39. 39.Is 112506 divisible by 24?
  40. 40.Is 8441 divisible by 23?

Answer key

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

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