# 189 and Level 4

 189 is a composite number. Factor pairs: 189 = 1 x 189, 3 x 63, 7 x 27, 9 x 21 Factors of 189: 1, 3, 7, 9, 21, 27, 63, 189 Prime factorization: 189 = 3 x 3 x 3 x 7, which can also be written 189 = (3^3) x 7

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

# 188 and Level 3

 188 is a composite number. Factor pairs: 188 = 1 x 188, 2 x 94, or 4 x 47 Factors of 188: 1, 2, 4, 47, 94, 188 Prime factorization: 188 = 2 x 2 x 47, which can be written 188 = (2^2) x 47

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

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.

# 187 and Level 2

 187 is a composite number. Factor pairs: 187 = 1 x 187 or 11 x 17 Factors of 187: 1, 11, 17, 187 Prime factorization: 187 = 11 x 17

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

# 186 and Level 1

 186 is a composite number. Factor pairs: 186 = 1 x 186, 2 x 93, 3 x 62, 6 x 31 Factors of 186: 1, 2, 3, 6, 31, 62, 93, 186 Prime factorization: 186 = 2 x 3 x 31

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

# 185 and Level 6

 185 is a composite number. Factor pairs: 185 = 1 x 185 or 5 x 37 Factors of 185: 1, 5, 37, 185 Prime factorization: 185 = 5 x 37

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

# 184 and Level 5

 184 is a composite number. Factor pairs: 184 = 1 x 184, 2 x 92, 4 x 46, or 8 x 23 Factors of 184: 1, 2, 4, 8, 23, 46, 92, 184 Prime factorization: 184 = 2 x 2 x 2 x 23, which can be written (2^3) x 23

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

# 183 and Level 4

 183 is a composite number. Factor pairs: 183 = 1 x 183 or 3 x 61 Factors of 183: 1, 3, 61, 183 Prime factorization: 183 = 3 x 61

Notice this for 183: 1 + 8 + 3 = 12 which is a multiple of 3, so 183 is also a multiple of 3.

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

# 182 and Level 3

 182 is a composite number. Factor pairs: 182 = 1 x 182, 2 x 91, 7 x 26, or 13 x 14 Factors of 182: 1, 2, 7, 13, 14, 26, 91, 182 Prime factorization: 182 = 2 x 7 x 13

Notice this for 182: 18 – (2 x 2) = 18 – 4 = 14, a multiple of 7, so 182 can be evenly divided by 7.

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

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.

# 181 and Level 2

• 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

# 180 and Level 1

 180 is a composite number. Factor pairs: 180 = 1 x 180, 2 x 90, 3 x 60, 4 x 45, 5 x 36, 6 x 30, 9 x 20, 10 x 18, or 12 x 15 Factors of 180: 1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 30, 36, 45, 60, 90, 180 Prime factorization: 180 = 2 x 2 x 3 x 3 x 5 which can be written 180 = (2^2) x (3^2) x 5

There are 180 degrees in a triangle.

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