270 and Level 2

  • 270 is a composite number.
  • Prime factorization: 270 = 2 x 3 x 3 x 3 x 5, which can be written 2 x (3^3) x 5
  • The exponents in the prime factorization are 1, 3, and 1. Adding one to each and multiplying we get (1 + 1)(3 + 1)(1 + 1) = 2 x 4 x 2 = 16. Therefore 270 has 16 factors.
  • Factors of 270: 1, 2, 3, 5, 6, 9, 10, 15, 18, 27, 30, 45, 54, 90, 135, 270
  • Factor pairs: 270 = 1 x 270, 2 x 135, 3 x 90, 5 x 54, 6 x 45, 9 x 30, 10 x 27, or 15 x 18
  • Taking the factor pair with the largest square number factor, we get √270 = (√9)(√30) = 3√30 ≈ 16.432

Can you solve this level 2 puzzle?

2014-42 Level 2

Print the puzzles or type the factors on this excel file: 12 Factors 2014-10-20

2014-42 Level 2 Factors

 

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