A Multiplication Based Logic Puzzle

674 and Level 1

674 is the hypotenuse of the Pythagorean triple 350-576-674. What is the greatest common factor of those three numbers?

674 is a leg in exactly one Pythagorean triple: 674-113568-113570, and those three numbers have the exact same greatest common factor as the triple above.

674 Puzzle

Print the puzzles or type the solution on this excel file: 10 Factors 2015-11-09

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  • 674 is a composite number.
  • Prime factorization: 674 = 2 x 337
  • The exponents in the prime factorization are 1 and 1. Adding one to each and multiplying we get (1 + 1)(1 + 1) = 2 x 2 = 4. Therefore 674 has exactly 4 factors.
  • Factors of 674: 1, 2, 337, 674
  • Factor pairs: 674 = 1 x 674 or 2 x 337
  • 674 has no square factors that allow its square root to be simplified. √674 ≈ 25.96151.

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674 Factors

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