A Multiplication Based Logic Puzzle

191 and Level 6

  • 191 is a prime number.
  • Prime factorization: 191 is prime.
  • The exponent of prime number 191 is 1. Adding 1 to that exponent we get (1 + 1) = 2. Therefore 191 has exactly 2 factors.
  • Factors of 191: 1, 191
  • Factor pairs: 191 = 1 x 191
  • 191 has no square factors that allow its square root to be simplified. √191 ≈ 13.82027

How do we know that 191 is a prime number? If 191 were not a prime number, then it would be divisible by at least one prime number less than or equal to √191 ≈ 13.8. Since 191 cannot be divided evenly by 2, 3, 5, 7, 11, or 13, we know that 191 is a prime number.

There are 22 prime numbers between 100 and 200:

  • The first four of those prime numbers are 101, 103, 107, and 109.
  • The last four of those prime numbers are 191, 193, 197, and 199.

 

2014-30 Level 6

Excel file of puzzles and previous week’s factor solutions: 12 Factors 2014-07-28

2014-30 Level 6 Logic

2014-30 Level 6 Problems

 

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