A Multiplication Based Logic Puzzle

Posts tagged ‘16’

A Forest of 240 Factor Trees

  • 240 is a composite number.
  • Prime factorization: 240 = 2 x 2 x 2 x 2 x 3 x 5, which can be written (2^4) x 3 x 5
  • The exponents in the prime factorization are 4, 1 and 1. Adding one to each and multiplying we get (4 + 1)(1 + 1)(1 + 1) = 5 x 2 x 2 = 20. Therefore 240 has 20 factors.
  • Factors of 240: 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 30, 40, 48, 60, 80, 120, 240
  • Factor pairs: 240 = 1 x 240, 2 x 120, 3 x 80, 4 x 60, 5 x 48, 6 x 40, 8 x 30, 10 x 24, 12 x 20, or 15 x 16
  • Taking the factor pair with the largest square number factor, we get √240 = (√16)(√15) = 4√15 ≈ 15.492.

Because 240 has so many factors, it is possible to make MANY different factor trees that create a forest of 240 factor trees. This post only contains eleven of those many possibilities. The two trees below demonstrate different permutations that can be made from the same basic tree. The mirror images of both, as well as mirror images of parts of either tree, would be other permutations.

240 Factor Trees

 

A good way to make a factor tree for a composite number is to begin with one of its factor pairs and then make factor trees for the composite numbers in that factor pair.

240 Factor Trees 1 - 3

In this first set of three factor trees we can also see the factor trees for 120, 80, 4, & 60.

240 Factor Trees 4 - 6

These three factor trees also include factor trees for 48, 6, 40, 8, and 30.

240 Factor Trees 7 - 9

Finally, these three factor trees also include factor trees for 10, 24, 12, 20, 15, and 16.

This forest of 240 factor trees is dedicated to Joseph Nebus. Read the comments to his post, You might also like, because, I don’t know why, to discover why I was inspired to create images of parts of this forest.

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16 Silver Bells

16 is a composite number, and it is 4 squared. 16 = 1 x 16, 2 x 8, or 4 x 4. Factors of 16: 1, 2, 4, 8, 16. Prime factorization: 16 = 2 x 2 x 2 x 2, which can also be written 16 = 2^4.

Since √16 = 4, a whole number, 16 is a perfect square.

When 16 is a clue in the FIND THE FACTORS puzzles, use either 2 x 8 or 4 x 4. Only one of those sets of factors will work for any particular puzzle.

Silver bells, silver bells.
It’s Christmas time in the city.

2013-12-16.42013-12-16.7

Find the Factors is a type of logic puzzle. To solve one of the above puzzles, place the numbers 1 – 10 in both the top row and in the first column so that those numbers are factors of the given clues. For each puzzle there is only one solution. Click on 10 Factors 2013-12-16 to find these and a few more puzzles, as well as last Monday’s solutions.

Some of these Related articles have the lyrics or soundtrack to Silver Bells:

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