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Divisibility Rules Worksheet

Vedic maths trick 13: Divisibility tests · Set 663 · 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 36072 divisible by 7?
  2. 2.Is 12675 divisible by 8?
  3. 3.Is 28605 divisible by 5?
  4. 4.Is 41020 divisible by 20?
  5. 5.Is 86108 divisible by 19?
  6. 6.Is 36024 divisible by 8?
  7. 7.Is 4356 divisible by 6?
  8. 8.Is 9123 divisible by 3?
  9. 9.Is 96335 divisible by 29?
  10. 10.Is 38225 divisible by 7?
  11. 11.Is 6488 divisible by 4?
  12. 12.Is 10973 divisible by 7?
  13. 13.Is 18923 divisible by 3?
  14. 14.Is 501 divisible by 3?
  15. 15.Is 4700 divisible by 4?
  16. 16.Is 3982 divisible by 11?
  17. 17.Is 30080 divisible by 7?
  18. 18.Is 72796 divisible by 17?
  19. 19.Is 125655 divisible by 18?
  20. 20.Is 80061 divisible by 24?
  21. 21.Is 67691 divisible by 13?
  22. 22.Is 24876 divisible by 4?
  23. 23.Is 84647 divisible by 15?
  24. 24.Is 12104 divisible by 17?
  25. 25.Is 17802 divisible by 4?
  26. 26.Is 41610 divisible by 7?
  27. 27.Is 34588 divisible by 7?
  28. 28.Is 58697 divisible by 10?
  29. 29.Is 36870 divisible by 10?
  30. 30.Is 15900 divisible by 10?
  31. 31.Is 44721 divisible by 9?
  32. 32.Is 139678 divisible by 23?
  33. 33.Is 27666 divisible by 29?
  34. 34.Is 6029 divisible by 23?
  35. 35.Is 58157 divisible by 11?
  36. 36.Is 89190 divisible by 24?
  37. 37.Is 59961 divisible by 23?
  38. 38.Is 36012 divisible by 20?
  39. 39.Is 1397 divisible by 11?
  40. 40.Is 628 divisible by 6?

Answer key

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

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