637 and Level 2

637 is the sum of two perfect squares, 441 and 196, so it is the hypotenuse of a Pythagorean triple, namely 245-588-637. The greatest common factor of those FIVE numbers is also a perfect square. What is it?

637 is the sum of the nineteen prime numbers from 3 to 71.

637 Puzzle

Print the puzzles or type the solution on this excel file: 12 Factors 2015-10-05

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  • 637 is a composite number.
  • Prime factorization: 637 = 7 x 7 x 13, which can be written 637 = (7^2) x 13
  • 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 637 has exactly 6 factors.
  • Factors of 637: 1, 7, 13, 49, 91, 637
  • Factor pairs: 637 = 1 x 637, 7 x 91, or 13 x 49
  • Taking the factor pair with the largest square number factor, we get √637 = (√49)(√13) = 7√13 ≈ 25.2388589.

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637 Factors

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