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Divisibility Rules Worksheet

Vedic maths trick 13: Divisibility tests · Set 471 · 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 5370 divisible by 9?
  2. 2.Is 37720 divisible by 10?
  3. 3.Is 53122 divisible by 13?
  4. 4.Is 20587 divisible by 23?
  5. 5.Is 13608 divisible by 8?
  6. 6.Is 33222 divisible by 11?
  7. 7.Is 21750 divisible by 15?
  8. 8.Is 18797 divisible by 30?
  9. 9.Is 19342 divisible by 3?
  10. 10.Is 900 divisible by 4?
  11. 11.Is 93616 divisible by 23?
  12. 12.Is 30682 divisible by 6?
  13. 13.Is 84981 divisible by 13?
  14. 14.Is 7804 divisible by 18?
  15. 15.Is 19836 divisible by 4?
  16. 16.Is 12343 divisible by 3?
  17. 17.Is 21846 divisible by 13?
  18. 18.Is 117248 divisible by 29?
  19. 19.Is 4518 divisible by 2?
  20. 20.Is 1769 divisible by 4?
  21. 21.Is 18668 divisible by 3?
  22. 22.Is 12616 divisible by 19?
  23. 23.Is 41747 divisible by 7?
  24. 24.Is 52272 divisible by 9?
  25. 25.Is 18151 divisible by 4?
  26. 26.Is 58698 divisible by 9?
  27. 27.Is 24650 divisible by 8?
  28. 28.Is 42000 divisible by 10?
  29. 29.Is 76445 divisible by 13?
  30. 30.Is 68797 divisible by 30?
  31. 31.Is 7186 divisible by 18?
  32. 32.Is 2485 divisible by 4?
  33. 33.Is 12549 divisible by 3?
  34. 34.Is 92920 divisible by 23?
  35. 35.Is 57249 divisible by 15?
  36. 36.Is 36930 divisible by 10?
  37. 37.Is 33605 divisible by 11?
  38. 38.Is 45266 divisible by 24?
  39. 39.Is 28177 divisible by 5?
  40. 40.Is 19903 divisible by 18?

Answer key

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

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