A Multiplication Based Logic Puzzle

216 and Level 4

  • 216 is a composite number.
  • 216 = 6 x 6 x 6, so it is a perfect cube, 6³.
  • Prime factorization: 216 = 2 x 2 x 2 x 3 x 3 x 3, which can be written 216 = 2³ x 3³.
  • The exponents in the prime factorization are 3 and 3. Adding one to each and multiplying we get (3 + 1) x (3 + 1) = 4 x 4 = 16. Therefore 216 has 16 factors.
  • Factors of 216: 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 27, 36, 54, 72, 108, 216
  • Factor pairs: 216 = 1 x 216, 2 x 108, 3 x 72, 4 x 54, 6 x 36, 8 x 27, 9 x 24, 12 x 18
  • Taking the factor pair with the largest square number factor, we get √216 = (√6)(√36) = 6√6 ≈ 14.697

It’s been a busy summer for me and lots of other people, yet Alan Parr found the time this summer to write a great post about the Find the Factors puzzles.  You can read it at established1962 find-the-factors.

2014-34 Level 4

Excel file of puzzles and previous week’s factor solutions: 12 Factors 2014-08-25

2014-34 Level 4 Logic

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