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Divisibility Rules Worksheet

Vedic maths trick 13: Divisibility tests · Set 273 · 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 71969 divisible by 19?
  2. 2.Is 84019 divisible by 23?
  3. 3.Is 14620 divisible by 4?
  4. 4.Is 22872 divisible by 24?
  5. 5.Is 114867 divisible by 23?
  6. 6.Is 14011 divisible by 12?
  7. 7.Is 24827 divisible by 11?
  8. 8.Is 41094 divisible by 30?
  9. 9.Is 42570 divisible by 24?
  10. 10.Is 30594 divisible by 30?
  11. 11.Is 150569 divisible by 24?
  12. 12.Is 49920 divisible by 24?
  13. 13.Is 8274 divisible by 2?
  14. 14.Is 109847 divisible by 24?
  15. 15.Is 62176 divisible by 9?
  16. 16.Is 41936 divisible by 30?
  17. 17.Is 63616 divisible by 10?
  18. 18.Is 197896 divisible by 29?
  19. 19.Is 105660 divisible by 29?
  20. 20.Is 677 divisible by 2?
  21. 21.Is 44298 divisible by 9?
  22. 22.Is 17572 divisible by 23?
  23. 23.Is 108740 divisible by 20?
  24. 24.Is 75280 divisible by 20?
  25. 25.Is 15650 divisible by 8?
  26. 26.Is 38545 divisible by 12?
  27. 27.Is 1668 divisible by 12?
  28. 28.Is 11781 divisible by 17?
  29. 29.Is 100970 divisible by 20?
  30. 30.Is 10873 divisible by 4?
  31. 31.Is 78030 divisible by 19?
  32. 32.Is 191550 divisible by 30?
  33. 33.Is 99349 divisible by 30?
  34. 34.Is 41895 divisible by 7?
  35. 35.Is 4728 divisible by 13?
  36. 36.Is 3976 divisible by 4?
  37. 37.Is 27662 divisible by 10?
  38. 38.Is 7032 divisible by 2?
  39. 39.Is 15303 divisible by 3?
  40. 40.Is 42946 divisible by 8?

Answer key

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

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