Final answer:
The factor pair of 72 that has a prime number is 2 x 36, as 2 is the only prime number listed among the pairs provided.
Step-by-step explanation:
The student has listed four factor pairs of 72: 2 x 36, 4 x 18, 6 x 12, and 8 x 9.
They want to identify which pair contains a prime number.
A prime number is a natural number greater than 1 that is not a product of two smaller natural numbers.
Looking at the pairs provided, we recognize that 2 is the only prime number listed because it can only be divided by 1 and itself.
Hence, the pair 2 x 36 contains a prime number.
The other numbers, 36, 4, 18, 6, 12, 8, and 9, are all composite numbers because they can be divided evenly by numbers other than 1 and themselves.