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Divisibility Rules Worksheet

Vedic maths trick 13: Divisibility tests · Set 419 · 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 2833 divisible by 3?
  2. 2.Is 6836 divisible by 5?
  3. 3.Is 17056 divisible by 7?
  4. 4.Is 408 divisible by 8?
  5. 5.Is 44433 divisible by 13?
  6. 6.Is 57600 divisible by 15?
  7. 7.Is 109217 divisible by 29?
  8. 8.Is 43101 divisible by 13?
  9. 9.Is 8668 divisible by 2?
  10. 10.Is 113802 divisible by 19?
  11. 11.Is 3500 divisible by 2?
  12. 12.Is 26580 divisible by 10?
  13. 13.Is 9215 divisible by 20?
  14. 14.Is 71808 divisible by 12?
  15. 15.Is 27485 divisible by 30?
  16. 16.Is 143496 divisible by 24?
  17. 17.Is 69692 divisible by 19?
  18. 18.Is 25210 divisible by 4?
  19. 19.Is 13372 divisible by 2?
  20. 20.Is 199320 divisible by 30?
  21. 21.Is 7223 divisible by 2?
  22. 22.Is 32269 divisible by 9?
  23. 23.Is 53138 divisible by 12?
  24. 24.Is 26184 divisible by 19?
  25. 25.Is 13700 divisible by 2?
  26. 26.Is 1114 divisible by 4?
  27. 27.Is 72753 divisible by 13?
  28. 28.Is 5514 divisible by 10?
  29. 29.Is 9040 divisible by 5?
  30. 30.Is 11816 divisible by 9?
  31. 31.Is 37069 divisible by 23?
  32. 32.Is 8396 divisible by 4?
  33. 33.Is 5529 divisible by 4?
  34. 34.Is 42739 divisible by 7?
  35. 35.Is 59330 divisible by 17?
  36. 36.Is 21980 divisible by 7?
  37. 37.Is 69744 divisible by 12?
  38. 38.Is 36204 divisible by 6?
  39. 39.Is 66628 divisible by 30?
  40. 40.Is 83610 divisible by 24?

Answer key

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

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