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Divisibility Rules Worksheet

Vedic maths trick 13: Divisibility tests · Set 747 · 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 45415 divisible by 7?
  2. 2.Is 9639 divisible by 6?
  3. 3.Is 14267 divisible by 11?
  4. 4.Is 84608 divisible by 13?
  5. 5.Is 22538 divisible by 30?
  6. 6.Is 7375 divisible by 3?
  7. 7.Is 30976 divisible by 5?
  8. 8.Is 13242 divisible by 2?
  9. 9.Is 23021 divisible by 5?
  10. 10.Is 33520 divisible by 10?
  11. 11.Is 16262 divisible by 8?
  12. 12.Is 30807 divisible by 5?
  13. 13.Is 47720 divisible by 20?
  14. 14.Is 5626 divisible by 11?
  15. 15.Is 2251 divisible by 6?
  16. 16.Is 12940 divisible by 5?
  17. 17.Is 56524 divisible by 13?
  18. 18.Is 60827 divisible by 13?
  19. 19.Is 2658 divisible by 2?
  20. 20.Is 17934 divisible by 6?
  21. 21.Is 105129 divisible by 20?
  22. 22.Is 55286 divisible by 11?
  23. 23.Is 32147 divisible by 17?
  24. 24.Is 48387 divisible by 8?
  25. 25.Is 176929 divisible by 29?
  26. 26.Is 43788 divisible by 12?
  27. 27.Is 197872 divisible by 30?
  28. 28.Is 42244 divisible by 9?
  29. 29.Is 23376 divisible by 12?
  30. 30.Is 15744 divisible by 24?
  31. 31.Is 19728 divisible by 18?
  32. 32.Is 3826 divisible by 7?
  33. 33.Is 112752 divisible by 18?
  34. 34.Is 79488 divisible by 18?
  35. 35.Is 14458 divisible by 3?
  36. 36.Is 3830 divisible by 9?
  37. 37.Is 26745 divisible by 5?
  38. 38.Is 14499 divisible by 9?
  39. 39.Is 12073 divisible by 3?
  40. 40.Is 9846 divisible by 3?

Answer key

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

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