# Which of the following numbers has the largest number of unique prime factors?: {85, 138, 317, 207}

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To determine which number has the largest number of unique prime factors among the given set, we can find the prime factorization of each number and count the unique prime factors.

Prime factorization of each number: 85 = 5 × 17 138 = 2 × 3 × 23 317 is a prime number, so its only prime factor is itself. 207 = 3 × 3 × 23

Count of unique prime factors: 85 has 2 unique prime factors. 138 has 3 unique prime factors. 317 has 1 unique prime factor. 207 has 2 unique prime factors.

Therefore, among the given numbers, 138 has the largest number of unique prime factors.

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