A Multiplication Based Logic Puzzle

340 and Level 5

  • 340 is a composite number.
  • Prime factorization: 340 = 2 x 2 x 5 x 17, which can be written 340 = (2^2) x 5 x 17
  • The exponents in the prime factorization are 2, 1, and 1. Adding one to each and multiplying we get (2 + 1)(1 + 1)(1 + 1) = 3 x 2 x 2 = 12. Therefore 340 has exactly 12 factors.
  • Factors of 340: 1, 2, 4, 5, 10, 17, 20, 34, 68, 85, 170, 340
  • Factor pairs: 340 = 1 x 340, 2 x 170, 4 x 85, 5 x 68, 10 x 34, or 17 x 20
  • Taking the factor pair with the largest square number factor, we get √340 = (√4)(√85) = 2√85 ≈ 18.439

Do you have any goals to improve your thinking power this year? Well, solving puzzles like this one can be good for your brain!

2014-52 Level 5

Print the puzzles or type the factors on this excel file: 12 Factors 2014-12-29

2014-52 Level 5 Logic

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