A Multiplication Based Logic Puzzle

  • 316 is a composite number.
  • Prime factorization: 316 = 2 x 2 x 79, which can be written 316 = (2^2) x 79
  • The exponents in the prime factorization are 2 and 1. Adding one to each and multiplying we get (2 + 1)(1 + 1) = 3 x 2  = 6. Therefore 316 has exactly 6 factors.
  • Factors of 316: 1, 2, 4, 79, 158, 316
  • Factor pairs: 316 = 1 x 316, 2 x 158, or 4 x 79
  • Taking the factor pair with the largest square number factor, we get √316 = (√4)(√79) = 2√79 ≈ 17.776.

Today is all about Christmas trees. You can read how one family set up a beautiful Christmas tree at three-things-thursday-tree-edition, solve the Christmas tree puzzle, and scroll down to see two possible factor trees for 316.

Then polish up your shoes and boots. Place them near your front door or window so they will be ready to be filled with treats when Mikulás (St. Nickolas) makes his rounds tonight.

2014-48 Level 5

Print the puzzles or type the factors on this excel file: 12 Factors 2014-12-01

2014-48 Level 5 Logic

316 Christmas Factor Trees

 

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