• 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