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Divisibility Rules Worksheet

Vedic maths trick 13: Divisibility tests · Set 768 · 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 21246 divisible by 19?
  2. 2.Is 8321 divisible by 4?
  3. 3.Is 45864 divisible by 9?
  4. 4.Is 78578 divisible by 12?
  5. 5.Is 61224 divisible by 12?
  6. 6.Is 16746 divisible by 17?
  7. 7.Is 100604 divisible by 24?
  8. 8.Is 8469 divisible by 9?
  9. 9.Is 8357 divisible by 12?
  10. 10.Is 11113 divisible by 2?
  11. 11.Is 21255 divisible by 5?
  12. 12.Is 51940 divisible by 20?
  13. 13.Is 9882 divisible by 3?
  14. 14.Is 27149 divisible by 17?
  15. 15.Is 4035 divisible by 23?
  16. 16.Is 7744 divisible by 8?
  17. 17.Is 27436 divisible by 19?
  18. 18.Is 32501 divisible by 7?
  19. 19.Is 720 divisible by 20?
  20. 20.Is 3608 divisible by 4?
  21. 21.Is 30582 divisible by 6?
  22. 22.Is 70482 divisible by 20?
  23. 23.Is 14649 divisible by 3?
  24. 24.Is 23193 divisible by 24?
  25. 25.Is 51165 divisible by 15?
  26. 26.Is 22853 divisible by 4?
  27. 27.Is 41448 divisible by 6?
  28. 28.Is 34345 divisible by 5?
  29. 29.Is 31578 divisible by 19?
  30. 30.Is 151512 divisible by 24?
  31. 31.Is 28836 divisible by 18?
  32. 32.Is 72127 divisible by 11?
  33. 33.Is 114325 divisible by 17?
  34. 34.Is 9792 divisible by 3?
  35. 35.Is 59142 divisible by 23?
  36. 36.Is 3316 divisible by 6?
  37. 37.Is 36012 divisible by 12?
  38. 38.Is 11473 divisible by 3?
  39. 39.Is 5511 divisible by 5?
  40. 40.Is 55976 divisible by 8?

Answer key

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

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