A Multiplication Based Logic Puzzle

161 and Level 1

 161 is a composite number. Factor pairs: 161 = 1 x 161 or 7 x 23 Factors of 161: 1, 7, 23, 161 Prime factorization: 161 = 7 x 23

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Excel file of puzzles and previous week’s factor solutions: 12 Factors 2014-06-30

160 and Level 6

 160 is a composite number. Factor pairs: 160 = 1 x 160, 2 x 80, 4 x 40, 5 x 32, 8 x 20, or 10 x 16 Factors of 160: 1, 2, 4, 5, 8, 10, 16, 20, 32, 40, 80, 160 Prime factorization: 160 = 2 x 2 x 2 x 2 x 2 x 5, which can also be written 160 = (2^5) x 5

160 = 2 + 3 + 5 + 7 + 11 + 13 + 17 + 19 + 23 + 29 + 31 (the sum of the first eleven prime numbers).

Excel file of puzzles and previous week’s factor solutions: 10 Factors 2014-06-23

159 and Level 5

 159 is a composite number. Factor pairs: 159 = 1 x 159 or 3 x 53 Factors of 159: 1, 3, 53, 159 Prime factorization: 159 = 3 x 53

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Excel file of puzzles and previous week’s factor solutions: 10 Factors 2014-06-23

158 and Level 4

 158 is a composite number. Factor pairs: 158 = 1 x 158 or 2 x 79 Factors of 158: 1, 2, 79, 158 Prime factorization: 158 = 2 x 79

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Excel file of puzzles and previous week’s factor solutions: 10 Factors 2014-06-23

157 and Level 3

157 is a prime number. Factor pairs: 157 = 1 x 157. Its only factors are 1 and 157. Prime factorization: none

How do we know that 157 is a prime number? The square root of 157 is an irrational number approximately equal to 12.53. If 157 were not a prime number, then it would be divisible by at least one prime number less than or equal to 12.53. Since 157 cannot be divided evenly by 2, 3, 5, 7, or 11, we know that 157 is a prime number.

Excel file of puzzles and previous week’s factor solutions: 10 Factors 2014-06-23

A Logical Approach to FIND THE FACTORS: Find the column or row with two clues and find their common factor. Write the corresponding factors in the factor column (1st column) and factor row (top row).  Because this is a level three puzzle, you have now written a factor at the top of the factor column. Continue to work from the top of the factor column to the bottom, finding factors and filling in the factor column and the factor row one cell at a time as you go.

156 and Level 2

 156 is a composite number. Factor pairs: 156 = 1 x 156, 2 x 78, 3 x 52, 4 x 39, 6 x 26, or 12 x 13 Factors of 156: 1, 2, 3, 4, 6, 12, 13, 26, 39, 52, 78, 156 Prime factorization: 156 = 2 x 2 x 3 x 13, which can be written (2^2) x 3 x 13

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Excel file of puzzles and previous week’s factor solutions: 10 Factors 2014-06-23

155 and Level 1

 155 is a composite number. Factor pairs: 155 = 1 x 155 or 5 x 31 Factors of 155: 1, 5, 31, 155 Prime factorization: 155 = 5 x 31

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Excel file of puzzles and previous week’s factor solutions: 10 Factors 2014-06-23