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Divisibility Rules Worksheet

Vedic maths trick 13: Divisibility tests · Set 271 · 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 13957 divisible by 2?
  2. 2.Is 147307 divisible by 30?
  3. 3.Is 9171 divisible by 9?
  4. 4.Is 126838 divisible by 19?
  5. 5.Is 5315 divisible by 5?
  6. 6.Is 55941 divisible by 17?
  7. 7.Is 172753 divisible by 29?
  8. 8.Is 17235 divisible by 15?
  9. 9.Is 17667 divisible by 13?
  10. 10.Is 22784 divisible by 24?
  11. 11.Is 110067 divisible by 17?
  12. 12.Is 88626 divisible by 17?
  13. 13.Is 41850 divisible by 15?
  14. 14.Is 37798 divisible by 7?
  15. 15.Is 88552 divisible by 29?
  16. 16.Is 170433 divisible by 29?
  17. 17.Is 111010 divisible by 17?
  18. 18.Is 31825 divisible by 19?
  19. 19.Is 3550 divisible by 6?
  20. 20.Is 5705 divisible by 8?
  21. 21.Is 130732 divisible by 23?
  22. 22.Is 96120 divisible by 18?
  23. 23.Is 35438 divisible by 13?
  24. 24.Is 86871 divisible by 23?
  25. 25.Is 2364 divisible by 4?
  26. 26.Is 30895 divisible by 7?
  27. 27.Is 2910 divisible by 6?
  28. 28.Is 12945 divisible by 5?
  29. 29.Is 21190 divisible by 18?
  30. 30.Is 1684 divisible by 3?
  31. 31.Is 44680 divisible by 8?
  32. 32.Is 123129 divisible by 24?
  33. 33.Is 2736 divisible by 6?
  34. 34.Is 22510 divisible by 5?
  35. 35.Is 14025 divisible by 3?
  36. 36.Is 31786 divisible by 8?
  37. 37.Is 10139 divisible by 2?
  38. 38.Is 5890 divisible by 3?
  39. 39.Is 111991 divisible by 20?
  40. 40.Is 15568 divisible by 8?

Answer key

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

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