• 197 is a prime number.
• Prime factorization: 197 is prime.
• The exponent of prime number 197 is 1. Adding 1 to that exponent we get (1 + 1) = 2. Therefore 197 has exactly 2 factors.
• Factors of 197: 1, 197
• Factor pairs: 197 = 1 x 197
• 197 has no square factors that allow its square root to be simplified. √197 ≈ 14.0356688

How do we know that 197 is a prime number? If 197 were not a prime number, then it would be divisible by at least one prime number less than or equal to √197 ≈ 14. Since 197 cannot be divided evenly by 2, 3, 5, 7, 11, or 13, we know that 197 is a prime number.

Excel file of puzzles and previous week’s factor solutions: 10 Factors 2014-08-04

• 193 is a prime number.
• Prime factorization: 193 is prime.
• The exponent of prime number 193 is 1. Adding 1 to that exponent we get (1 + 1) = 2. Therefore 193 has exactly 2 factors.
• Factors of 193: 1, 193
• Factor pairs: 193 = 1 x 193
• 193 has no square factors that allow its square root to be simplified. √193 ≈ 13.89244

How do we know that 193 is a prime number? If 193 were not a prime number, then it would be divisible by at least one prime number less than or equal to √193 ≈ 13.9. Since 193 cannot be divided evenly by 2, 3, 5, 7, 11, or 13, we know that 193 is a prime number.

Excel file of puzzles and previous week’s factor solutions: 10 Factors 2014-08-04

• 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.

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

• 181 is a prime number.
• Prime factorization: 181 is prime.
• The exponent of prime number 181 is 1. Adding 1 to that exponent we get (1 + 1) = 2. Therefore 181 has exactly 2 factors.
• Factors of 181: 1, 181
• Factor pairs: 181 = 1 x 181
• 181 has no square factors that allow its square root to be simplified. √181 ≈ 13.45362

How do we know that 181 is a prime number? If 181 were not a prime number, then it would be divisible by at least one prime number less than or equal to √181 ≈ 13.5. Since 181 cannot be divided evenly by 2, 3, 5, 7, 11, or 13, we know that 181 is a prime number.

Excel file of puzzles and previous week’s factor solutions: 10 Factors 2014-07-21

• 179 is a prime number.
• Prime factorization: 179 is prime.
• The exponent of prime number 179 is 1. Adding 1 to that exponent we get (1 + 1) = 2. Therefore 179 has exactly 2 factors.
• Factors of 179: 1, 179
• Factor pairs: 179 = 1 x 179
• 179 has no square factors that allow its square root to be simplified. √179 ≈ 13.379088

How do we know that 179 is a prime number? If 179 were not a prime number, then it would be divisible by at least one prime number less than or equal to √179 ≈ 13.4. Since 179 cannot be divided evenly by 2, 3, 5, 7, 11, or 13, we know that 179 is a prime number.

Excel file of puzzles and previous week’s factor solutions: 12 Factors 2014-07-14