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Divisibility Rules Worksheet

Vedic maths trick 13: Divisibility tests · Set 257 · 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 28967 divisible by 13?
  2. 2.Is 22616 divisible by 20?
  3. 3.Is 9125 divisible by 5?
  4. 4.Is 144540 divisible by 30?
  5. 5.Is 2460 divisible by 12?
  6. 6.Is 2178 divisible by 2?
  7. 7.Is 103619 divisible by 24?
  8. 8.Is 6286 divisible by 7?
  9. 9.Is 45685 divisible by 7?
  10. 10.Is 1330 divisible by 12?
  11. 11.Is 35097 divisible by 23?
  12. 12.Is 37194 divisible by 30?
  13. 13.Is 79038 divisible by 18?
  14. 14.Is 35562 divisible by 6?
  15. 15.Is 9816 divisible by 4?
  16. 16.Is 37816 divisible by 8?
  17. 17.Is 17808 divisible by 12?
  18. 18.Is 73574 divisible by 20?
  19. 19.Is 84213 divisible by 20?
  20. 20.Is 9912 divisible by 7?
  21. 21.Is 18432 divisible by 3?
  22. 22.Is 10376 divisible by 4?
  23. 23.Is 45930 divisible by 10?
  24. 24.Is 105404 divisible by 30?
  25. 25.Is 10234 divisible by 4?
  26. 26.Is 20876 divisible by 4?
  27. 27.Is 2232 divisible by 12?
  28. 28.Is 2177 divisible by 7?
  29. 29.Is 22510 divisible by 5?
  30. 30.Is 16755 divisible by 15?
  31. 31.Is 4968 divisible by 23?
  32. 32.Is 18102 divisible by 3?
  33. 33.Is 6483 divisible by 3?
  34. 34.Is 43983 divisible by 9?
  35. 35.Is 6912 divisible by 4?
  36. 36.Is 29033 divisible by 5?
  37. 37.Is 20070 divisible by 15?
  38. 38.Is 14832 divisible by 4?
  39. 39.Is 28920 divisible by 10?
  40. 40.Is 37344 divisible by 24?

Answer key

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

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