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Divisibility Rules Worksheet

Vedic maths trick 13: Divisibility tests · Set 574 · 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 6693 divisible by 2?
  2. 2.Is 71580 divisible by 20?
  3. 3.Is 143630 divisible by 24?
  4. 4.Is 44898 divisible by 17?
  5. 5.Is 10729 divisible by 2?
  6. 6.Is 35932 divisible by 13?
  7. 7.Is 4030 divisible by 9?
  8. 8.Is 98976 divisible by 24?
  9. 9.Is 169380 divisible by 30?
  10. 10.Is 28845 divisible by 7?
  11. 11.Is 86798 divisible by 18?
  12. 12.Is 29995 divisible by 9?
  13. 13.Is 85100 divisible by 23?
  14. 14.Is 10875 divisible by 29?
  15. 15.Is 7809 divisible by 2?
  16. 16.Is 45542 divisible by 7?
  17. 17.Is 13518 divisible by 6?
  18. 18.Is 19745 divisible by 3?
  19. 19.Is 33350 divisible by 5?
  20. 20.Is 1049 divisible by 3?
  21. 21.Is 30131 divisible by 13?
  22. 22.Is 13454 divisible by 7?
  23. 23.Is 12699 divisible by 9?
  24. 24.Is 25670 divisible by 17?
  25. 25.Is 46172 divisible by 7?
  26. 26.Is 6552 divisible by 4?
  27. 27.Is 1243 divisible by 4?
  28. 28.Is 112551 divisible by 20?
  29. 29.Is 8989 divisible by 2?
  30. 30.Is 80396 divisible by 29?
  31. 31.Is 4890 divisible by 5?
  32. 32.Is 42037 divisible by 12?
  33. 33.Is 48287 divisible by 10?
  34. 34.Is 73459 divisible by 13?
  35. 35.Is 65289 divisible by 19?
  36. 36.Is 36677 divisible by 11?
  37. 37.Is 88587 divisible by 17?
  38. 38.Is 173269 divisible by 30?
  39. 39.Is 54054 divisible by 9?
  40. 40.Is 44319 divisible by 17?

Answer key

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

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