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Divisibility Rules Worksheet

Vedic maths trick 13: Divisibility tests · Set 895 · 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 18855 divisible by 30?
  2. 2.Is 29117 divisible by 11?
  3. 3.Is 35112 divisible by 11?
  4. 4.Is 6252 divisible by 4?
  5. 5.Is 11420 divisible by 20?
  6. 6.Is 23709 divisible by 6?
  7. 7.Is 7897 divisible by 20?
  8. 8.Is 35397 divisible by 23?
  9. 9.Is 46020 divisible by 13?
  10. 10.Is 110626 divisible by 20?
  11. 11.Is 123246 divisible by 18?
  12. 12.Is 29625 divisible by 7?
  13. 13.Is 84702 divisible by 19?
  14. 14.Is 10361 divisible by 2?
  15. 15.Is 24845 divisible by 5?
  16. 16.Is 24710 divisible by 10?
  17. 17.Is 4675 divisible by 17?
  18. 18.Is 111091 divisible by 29?
  19. 19.Is 13365 divisible by 2?
  20. 20.Is 9482 divisible by 15?
  21. 21.Is 8779 divisible by 6?
  22. 22.Is 703 divisible by 2?
  23. 23.Is 46417 divisible by 7?
  24. 24.Is 127360 divisible by 19?
  25. 25.Is 60873 divisible by 12?
  26. 26.Is 78676 divisible by 13?
  27. 27.Is 35538 divisible by 6?
  28. 28.Is 25658 divisible by 20?
  29. 29.Is 20784 divisible by 24?
  30. 30.Is 30806 divisible by 5?
  31. 31.Is 11678 divisible by 23?
  32. 32.Is 12640 divisible by 20?
  33. 33.Is 65400 divisible by 30?
  34. 34.Is 6569 divisible by 2?
  35. 35.Is 9226 divisible by 3?
  36. 36.Is 42264 divisible by 24?
  37. 37.Is 21520 divisible by 10?
  38. 38.Is 22339 divisible by 24?
  39. 39.Is 26784 divisible by 8?
  40. 40.Is 10818 divisible by 11?

Answer key

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

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