A Multiplication Based Logic Puzzle

308 and Level 6

  • 308 is a composite number.
  • Prime factorization: 308 = 2 x 2 x 7 x 11, which can be written 308 = (2^2) x 7 x 11
  • 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 308 has exactly 12 factors.
  • Factors of 308: 1, 2, 4, 7, 11, 14, 22, 28, 44, 77, 154, 308
  • Factor pairs: 308 = 1 x 308, 2 x 154, 4 x 77, 7 x 44, 11 x 28, or 14 x 22
  • Taking the factor pair with the largest square number factor, we get √308 = (√4)(√77) = 2√77 ≈ 17.5499

2014-47 Level 6

Print the puzzles or type the factors on this excel file: 10 Factors 2014-11-24

2014-47 Level 6 Logic

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