## A Multiplication Based Logic Puzzle

### 149 and Level 2

149 is a prime number. Factor pairs: 149 = 1 x 149. Its only factors are 1 and 149. Prime factorization: none.

How do we know that 149 is a prime number? The square root of 149 is an irrational number approximately equal to 12.21. If 149 were not a prime number, then it would be divisible by at least one prime number less than or equal to 12.21. Since 149 cannot be divided evenly by 2, 3, 5, 7, or 11, we know that 149 is a prime number.

Excel file of puzzles and previous week’s factor solutions: 12 Factors 2014-06-16

### 139 and Level 5

139 is a prime number. Factor pairs: 139 = 1 x 139. Its only factors are 1 and 39. Prime factorization: none.

How do we know that 139 is a prime number? The square root of 139 is an irrational number approximately equal to 11.79. If 139 were not a prime number, then it would be divisible by at least one prime number less than or equal to 11.79. Since 139 cannot be divided evenly by 2, 3, 5, 7, or 11, we know that 139 is a prime number.

139 is never a clue in the FIND THE FACTORS puzzles.

Excel file with puzzles and the previous week’s factor solutions: 12 Factors 2014-06-02

### 137 and Level 4

137 is a prime number. Factor pairs: 137 = 1 x 137. Its only factors are 1 and 137. Prime factorization: none.

How do we know that 137 is a prime number? The square root of 137 is an irrational number approximately equal to 11.7047. If 137 were not a prime number, then it would be divisible by at least one prime number less than or equal to 11.7047. Since 137 cannot be divided evenly by 2, 3, 5, 7, or 11, we know that 137 is a prime number.

137 is never a clue in the FIND THE FACTORS puzzles.

Excel file with puzzles and the previous week’s factor solutions: 12 Factors 2014-06-02

### 131 and Level 4

131 is a prime number. 131 = 1 x 131. Its only factors are 1 and 131. Prime factorization: none.

How do we know that 131 is a prime number? The square root of 131 is an irrational number approximately equal to 11.45. If 131 were not a prime number, then it would be divisible by at least one prime number less than or equal to 11.45. Since 131 cannot be divided evenly by 2, 3, 5, 7, or 11, we know that 131 is a prime number.

131 is never a clue in the FIND THE FACTORS puzzles.

Excel file of puzzles and previous week’s solutions: 10 Factors 2014-05-26