A Multiplication Based Logic Puzzle

746 and Level 1

  • 746 is a composite number.
  • Prime factorization: 746 = 2 x 373
  • 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 746 has exactly 4 factors.
  • Factors of 746: 1, 2, 373, 746
  • Factor pairs: 746 = 1 x 746 or 2 x 373
  • 746 has no square factors that allow its square root to be simplified. √746 ≈ 27.313000567.

746-factor-pairs

Here’s today’s puzzle:

746 Puzzle

Print the puzzles or type the solution on this excel file: 10 Factors 2016-01-18

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Here’s a little more about the number 746:

746 is the sum of 4 consecutive numbers: 185 + 186 + 187 + 188 = 746.

746 is the hypotenuse of a Pythagorean triple triangle because 504² + 550² = 746².

746 is also the sum of three squares six different ways:

  •  27² + 4² + 1² = 746
  • 24² + 13² + 1² = 746
  • 24² + 11² + 7² = 746
  • 21² + 17² + 4² = 746
  • 21² + 16² + 7² = 746
  • 20² + 15² + 11² = 746

Stetson.edu shared this fun number fact: 1^7 + 2^4 + 3^6 = 746.

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746 Factors

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