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Divisibility Rules Worksheet

Vedic maths trick 13: Divisibility tests · Set 614 · 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 10314 divisible by 2?
  2. 2.Is 27445 divisible by 6?
  3. 3.Is 1242 divisible by 23?
  4. 4.Is 94569 divisible by 29?
  5. 5.Is 37532 divisible by 6?
  6. 6.Is 3744 divisible by 9?
  7. 7.Is 32510 divisible by 10?
  8. 8.Is 8805 divisible by 6?
  9. 9.Is 126005 divisible by 29?
  10. 10.Is 55011 divisible by 8?
  11. 11.Is 98693 divisible by 20?
  12. 12.Is 74464 divisible by 13?
  13. 13.Is 15291 divisible by 19?
  14. 14.Is 34024 divisible by 13?
  15. 15.Is 127939 divisible by 19?
  16. 16.Is 7890 divisible by 3?
  17. 17.Is 29801 divisible by 12?
  18. 18.Is 62463 divisible by 10?
  19. 19.Is 62586 divisible by 18?
  20. 20.Is 72056 divisible by 18?
  21. 21.Is 8890 divisible by 3?
  22. 22.Is 135642 divisible by 20?
  23. 23.Is 209940 divisible by 30?
  24. 24.Is 58409 divisible by 9?
  25. 25.Is 21744 divisible by 6?
  26. 26.Is 2448 divisible by 10?
  27. 27.Is 17940 divisible by 23?
  28. 28.Is 16876 divisible by 5?
  29. 29.Is 798 divisible by 12?
  30. 30.Is 32573 divisible by 5?
  31. 31.Is 53172 divisible by 24?
  32. 32.Is 23825 divisible by 4?
  33. 33.Is 11506 divisible by 13?
  34. 34.Is 49341 divisible by 23?
  35. 35.Is 14880 divisible by 4?
  36. 36.Is 23797 divisible by 4?
  37. 37.Is 76650 divisible by 19?
  38. 38.Is 169950 divisible by 30?
  39. 39.Is 12622 divisible by 10?
  40. 40.Is 45321 divisible by 7?

Answer key

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

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