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Divisibility Rules Worksheet

Vedic maths trick 13: Divisibility tests · Set 261 · 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 22913 divisible by 4?
  2. 2.Is 10457 divisible by 4?
  3. 3.Is 1599 divisible by 4?
  4. 4.Is 12231 divisible by 2?
  5. 5.Is 65057 divisible by 11?
  6. 6.Is 130485 divisible by 20?
  7. 7.Is 22876 divisible by 29?
  8. 8.Is 13975 divisible by 5?
  9. 9.Is 11032 divisible by 7?
  10. 10.Is 100944 divisible by 18?
  11. 11.Is 28628 divisible by 10?
  12. 12.Is 1287 divisible by 11?
  13. 13.Is 24210 divisible by 12?
  14. 14.Is 42019 divisible by 10?
  15. 15.Is 100439 divisible by 29?
  16. 16.Is 11858 divisible by 2?
  17. 17.Is 111806 divisible by 24?
  18. 18.Is 124080 divisible by 24?
  19. 19.Is 68839 divisible by 23?
  20. 20.Is 15143 divisible by 11?
  21. 21.Is 46800 divisible by 18?
  22. 22.Is 30273 divisible by 10?
  23. 23.Is 10821 divisible by 29?
  24. 24.Is 177596 divisible by 30?
  25. 25.Is 17659 divisible by 3?
  26. 26.Is 22909 divisible by 6?
  27. 27.Is 16992 divisible by 24?
  28. 28.Is 20094 divisible by 17?
  29. 29.Is 18755 divisible by 4?
  30. 30.Is 10924 divisible by 29?
  31. 31.Is 54572 divisible by 10?
  32. 32.Is 3737 divisible by 2?
  33. 33.Is 49918 divisible by 11?
  34. 34.Is 39893 divisible by 8?
  35. 35.Is 57913 divisible by 29?
  36. 36.Is 16800 divisible by 18?
  37. 37.Is 80123 divisible by 19?
  38. 38.Is 6357 divisible by 7?
  39. 39.Is 135861 divisible by 23?
  40. 40.Is 67776 divisible by 24?

Answer key

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

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