2-0+9=11 so 209 is divisible by 11.

• 209 is a composite number.
• Prime factorization: 209 = 11 x 19
• The exponents in the prime factorization are 1 and 1. Adding one to each and multiplying we get (1 + 1)(1 + 1) = 2 x 2 = 4. Therefore 209 has exactly 4 factors.
• Factors of 209: 1, 11, 19, 209
• Factor pairs: 209 = 1 x 209 or 11 x 19
• 209 has no square factors that allow its square root to be simplified. √209 ≈ 14.456832

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Excel file of puzzles and previous week’s factor solutions: 10 Factors 2014-08-18

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.

• 208 is a composite number.
• Prime factorization: 208 = 2 x 2 x 2 x 2 x 13, which can be written 208 = 2⁴ x 13
• The exponents in the prime factorization are 4 and 1. Adding one to each and multiplying we get (4 + 1)(1 + 1) = 5 x 2 = 10. Therefore 208 has exactly 10 factors.
• Factors of 208: 1, 2, 4, 8, 13, 16, 26, 52, 104, 208
• Factor pairs: 208 = 1 x 208, 2 x 104, 4 x 52, 8 x 26, or 13 x 16
• Taking the factor pair with the largest square number factor, we get √208 = (√16)(√13) = 4√13 ≈ 14.422205

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Excel file of puzzles and previous week’s factor solutions: 10 Factors 2014-08-18

• 207 is a composite number.
• Prime factorization: 207 = 3 x 3 x 23, which can be written 207 = 3² x 23
• The exponents in the prime factorization are 2 and 1. Adding one to each and multiplying we get (2 + 1)(1 + 1) = 3 x 2  = 6. Therefore 207 has exactly 6 factors.
• Factors of 207: 1, 3, 9, 23, 69, 207
• Factor pairs: 207 = 1 x 207, 3 x 69, or 9 x 23
• Taking the factor pair with the largest square number factor, we get √207 = (√9)(√23) = 3√23 ≈ 14.38749

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Excel file of puzzles and previous week’s factor solutions: 10 Factors 2014-08-18

• 206 is a composite number.
• Prime factorization: 206 = 2 x 103
• The exponents in the prime factorization are 1 and 1. Adding one to each and multiplying we get (1 + 1)(1 + 1) = 2 x 2 = 4. Therefore 206 has exactly 4 factors.
• Factors of 206: 1, 2, 103, 206
• Factor pairs: 206 = 1 x 206 or 2 x 103
• 206 has no square factors that allow its square root to be simplified. √206 ≈ 14.35270009

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Excel file of puzzles and previous week’s factor solutions: 12 Factors 2014-08-11

• 205 is a composite number.
• Prime factorization: 205 = 5 x 41
• The exponents in the prime factorization are 1 and 1. Adding one to each and multiplying we get (1 + 1)(1 + 1) = 2 x 2 = 4. Therefore 205 has exactly 4 factors.
• Factors of 205: 1, 5, 41, 205
• Factor pairs: 205 = 1 x 205 or 5 x 41
• 205 has no square factors that allow its square root to be simplified. √205 ≈ 14.317821

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Excel file of puzzles and previous week’s factor solutions: 12 Factors 2014-08-11

• 204 is a composite number.
• Prime factorization: 204 = 2 × 2 × 3 × 17, which can be written 204 = 2² × 3 × 17
• The exponents in the prime factorization are 2, 1, and 1. Adding one to each and multiplying we get (2 + 1)(1 + 1)(1 + 1) = 3 x 2 x 2 = 12. Therefore 204 has exactly 12 factors.
• Factors of 204: 1, 2, 3, 4, 6, 12, 17, 34, 51, 68, 102, 204
• Factor pairs: 204 = 1 x 204, 2 x 102, 3 x 68, 4 x 51, 6 x 34, or 12 x 17
• Taking the factor pair with the largest square number factor, we get √204 = (√4)(√51) = 2√51 ≈ 14.2828568570856999959987996

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Excel file of puzzles and previous week’s factor solutions: 12 Factors 2014-08-11

• 203 is a composite number.
• Prime factorization: 203 = 7 x 29
• The exponents in the prime factorization are 1 and 1. Adding one to each and multiplying we get (1 + 1)(1 + 1) = 2 x 2 = 4. Therefore 203 has exactly 4 factors.
• Factors of 203: 1, 7, 29, 203
• Factor pairs: 203 = 1 x 203 or 7 x 29
• 203 has no square factors that allow its square root to be simplified. √203 ≈ 14.2478068

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Excel file of puzzles and previous week’s factor solutions: 12 Factors 2014-08-11

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.

• 202 is a composite number.
• Prime factorization: 202 = 2 x 101
• The exponents in the prime factorization are 1 and 1. Adding one to each and multiplying we get (1 + 1)(1 + 1) = 2 x 2 = 4. Therefore 202 has exactly 4 factors.
• Factors of 202: 1, 2, 101, 202
• Factor pairs: 202 = 1 x 202 or 2 x 101
• 202 has no square factors that allow its square root to be simplified. √202 ≈ 14.2126704

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Excel file of puzzles and previous week’s factor solutions: 12 Factors 2014-08-11