## A Multiplication Based Logic Puzzle

### 199 and My List of Multiplication Rhymes

 199 is a prime number. Factor pairs: 199 = 1 x 199 Factors of 199: 1, 199 Prime factorization: none

How do we know that 199 is a prime number? The square root of 199 is an irrational number approximately equal to 14.11. If 199 were not a prime number, then it would be divisible by at least one prime number less than or equal to 14.11. Since 199 cannot be divided evenly by 2, 3, 5, 7, 11, or 13, we know that 199 is a prime number.

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I recently wrote a post that asked “Are Multiplication Rhymes Able to Help Kids Learn the Multiplication Table?” No list is perfect, but here is a list of rhymes that I’ve put together.

Most of the rhymes have rhyming clues to help students remember both numbers being multiplied as well as their product. I wrote the rhymes that are highlighted in yellow. Those highlighted in peach, purple, or blue are from other sources, but I did alter the rhymes for 24, 28, and 81. A black and white pdf of the rhymes is also available here.

### 197 and Level 5

 197 is a prime number. Factor pairs: 197 = 1 x 197 Factors of 197: 1, 197 Prime factorization: none

How do we know that 197 is a prime number? The square root of 197 is an irrational number approximately equal to 14.04. If 197 were not a prime number, then it would be divisible by at least one prime number less than or equal to 14.04. 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 and Level 2

 193 is a prime number. Factor pairs: 193 = 1 x 193 Factors of 193: 1, 193 Prime factorization: none

How do we know that 193 is a prime number? The square root of 193 is an irrational number approximately equal to 13.89. If 193 were not a prime number, then it would be divisible by at least one prime number less than or equal to 13.89. 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 and Level 6

 191 is a prime number. Factor pairs: 191 = 1 x 191 Factors of 191: 1, 191 Prime factorization: none
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 There are 22 prime numbers between 100 and 200. The first four prime numbers greater than 100 are 101, 103, 107, and 109. The last four prime numbers less than 200 are 191, 193, 197, and 199.

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How do we know that 191 is a prime number? The square root of 191 is an irrational number approximately equal to 13.82. If 191 were not a prime number, then it would be divisible by at least one prime number less than or equal to 13.82. Since 191 cannot be divided evenly by 2, 3, 5, 7, 11, or 13, we know that 191 is a prime number.

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

### 181 and Level 2

 181 is a prime number. Factor pairs: 181 = 1 x 181 Factors of 181: 1, 181 Prime factorization: none

How do we know that 181 is a prime number? The square root of 181 is an irrational number approximately equal to 13.45. If 181 were not a prime number, then it would be divisible by at least one prime number less than or equal to 13.45. 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 and Level 6

 179 is a prime number. Factor pairs: 179 = 1 x 179 Factors of 179: 1, 179 Prime factorization: none

How do we know that 179 is a prime number? The square root of 179 is an irrational number approximately equal to 13.38. If 179 were not a prime number, then it would be divisible by at least one prime number less than or equal to 13.38. 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