A Multiplication Based Logic Puzzle

Posts tagged ‘815’

815 and Level 1

Since multi-digit 815 ends with 5, it is a composite number, and it is also the hypotenuse of a Pythagorean triple:

  • 489-652-815 which is 163 times 3-4-5.

Can you write the numbers 1 – 12 in both the first column and the top row so that this puzzle functions like a multiplication table?

 

  • 815 is a composite number.
  • Prime factorization: 815 = 5 x 163
  • 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 815 has exactly 4 factors.
  • Factors of 815: 1, 5, 163, 815
  • Factor pairs: 815 = 1 x 815 or 5 x 163
  • 815 has no square factors that allow its square root to be simplified. √815 ≈ 5482048.

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