A Multiplication Based Logic Puzzle

641 and Level 6

(25^2) + (4^2) = 641

641 is the hypotenuse of the primitive Pythagorean triple 200-609-641 which was calculated using 2(25)(4), (25^2) – (4^2), and (25^2) + (4^2) .

 641 Puzzle

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

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  • 641 is a prime number.
  • Prime factorization: 641 is prime and cannot be factored.
  • The exponent of prime number 641 is 1. Adding 1 to that exponent we get (1 + 1) = 2. Therefore 641 has exactly 2 factors.
  • Factors of 641: 1, 641
  • Factor pairs: 641 = 1 x 641
  • 641 has no square factors that allow its square root to be simplified. √641 ≈ 25.3179778.

How do we know that 641 is a prime number? If 641 were not a prime number, then it would be divisible by at least one prime number less than or equal to √641 ≈ 25.3. Since 641 cannot be divided evenly by 2, 3, 5, 7, 11, 13, 17, 19, or 23, we know that 641 is a prime number.

Here’s another way we know that 641 is a prime number: Since (25^2) + (4^2) = 641, an odd number, and 25 and 4 have no common prime factors, we know that 641 is a prime number simply because it is not divisible by 5, 13, or 17.

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641 Logic

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