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Divisibility Rules Worksheet

Vedic maths trick 13: Divisibility tests · Set 513 · 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 9857 divisible by 4?
  2. 2.Is 14636 divisible by 6?
  3. 3.Is 56714 divisible by 17?
  4. 4.Is 27864 divisible by 6?
  5. 5.Is 5770 divisible by 18?
  6. 6.Is 26219 divisible by 8?
  7. 7.Is 6929 divisible by 11?
  8. 8.Is 21474 divisible by 6?
  9. 9.Is 21180 divisible by 10?
  10. 10.Is 97461 divisible by 17?
  11. 11.Is 76378 divisible by 13?
  12. 12.Is 80474 divisible by 23?
  13. 13.Is 1929 divisible by 4?
  14. 14.Is 152868 divisible by 24?
  15. 15.Is 72292 divisible by 11?
  16. 16.Is 22092 divisible by 12?
  17. 17.Is 24851 divisible by 5?
  18. 18.Is 35550 divisible by 30?
  19. 19.Is 13694 divisible by 7?
  20. 20.Is 93960 divisible by 18?
  21. 21.Is 2170 divisible by 5?
  22. 22.Is 13423 divisible by 2?
  23. 23.Is 8500 divisible by 2?
  24. 24.Is 33691 divisible by 5?
  25. 25.Is 7364 divisible by 7?
  26. 26.Is 10963 divisible by 5?
  27. 27.Is 33980 divisible by 8?
  28. 28.Is 12270 divisible by 6?
  29. 29.Is 128063 divisible by 24?
  30. 30.Is 35872 divisible by 19?
  31. 31.Is 97004 divisible by 17?
  32. 32.Is 4616 divisible by 19?
  33. 33.Is 12310 divisible by 5?
  34. 34.Is 3066 divisible by 2?
  35. 35.Is 6555 divisible by 19?
  36. 36.Is 19080 divisible by 15?
  37. 37.Is 88918 divisible by 23?
  38. 38.Is 6095 divisible by 2?
  39. 39.Is 59488 divisible by 17?
  40. 40.Is 4872 divisible by 8?

Answer key

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

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