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Among the factor pairs of 72 that Jesse listed:
1. \(2 \times 36\) (2 is prime)
2. \(4 \times 18\) (neither is prime)
3. \(6 \times 12\) (neither is prime)
4. \(8 \times 9\) (neither is prime)
The factor pair \(2 \times 36\) includes the prime number 2. Therefore, this is the factor pair that contains a prime number.