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Divisibility Rules Worksheet

Vedic maths trick 13: Divisibility tests · Set 561 · 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 44920 divisible by 20?
  2. 2.Is 61331 divisible by 23?
  3. 3.Is 10307 divisible by 8?
  4. 4.Is 40288 divisible by 13?
  5. 5.Is 14882 divisible by 4?
  6. 6.Is 32683 divisible by 17?
  7. 7.Is 55064 divisible by 18?
  8. 8.Is 14322 divisible by 23?
  9. 9.Is 76703 divisible by 20?
  10. 10.Is 7265 divisible by 20?
  11. 11.Is 131910 divisible by 23?
  12. 12.Is 58120 divisible by 24?
  13. 13.Is 50104 divisible by 9?
  14. 14.Is 110600 divisible by 19?
  15. 15.Is 33285 divisible by 15?
  16. 16.Is 52489 divisible by 24?
  17. 17.Is 48885 divisible by 7?
  18. 18.Is 63183 divisible by 11?
  19. 19.Is 24540 divisible by 20?
  20. 20.Is 45240 divisible by 30?
  21. 21.Is 5577 divisible by 13?
  22. 22.Is 7075 divisible by 15?
  23. 23.Is 9981 divisible by 30?
  24. 24.Is 19501 divisible by 30?
  25. 25.Is 1674 divisible by 2?
  26. 26.Is 44080 divisible by 20?
  27. 27.Is 10952 divisible by 30?
  28. 28.Is 4858 divisible by 13?
  29. 29.Is 68976 divisible by 24?
  30. 30.Is 127920 divisible by 24?
  31. 31.Is 20802 divisible by 3?
  32. 32.Is 62009 divisible by 9?
  33. 33.Is 8008 divisible by 4?
  34. 34.Is 19025 divisible by 9?
  35. 35.Is 8900 divisible by 10?
  36. 36.Is 11100 divisible by 20?
  37. 37.Is 34022 divisible by 23?
  38. 38.Is 13340 divisible by 17?
  39. 39.Is 56625 divisible by 15?
  40. 40.Is 79222 divisible by 24?

Answer key

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

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