Final answer:
The two 2-digit numbers that have a GCD of 6 and a product of 2880 are 36 and 80, which correspond to option c.
Step-by-step explanation:
We can find the two numbers by factorizing 2880 and then looking for two factors that match the criteria. First, the prime factorization of 2880 is 27 × 32 × 5. To have a GCD of 6, the numbers must each have one factor of 2 and one factor of 3, because 6 is 2 × 3. The remaining factors must be split between the two numbers such that their product is 2880 and they remain 2-digit numbers. Let's analyze the given options: 24 and 120 (24 is a 2-digit number with a prime factorization of 23 × 3 and 120 is a 3-digit number). 18 and 160 (18 has a prime factorization of 2 × 32 and 160 is a 3-digit number). 36 and 80 (36 has a prime factorization of 22 × 32 and 80 is 24 × 5, and their product is 2880). 42 and 90 (42 is a 2-digit number, but the product with 90 does not equal 2880). Thus, option c, with the numbers 36 and 80, is the correct pair. These numbers have a GCD of 6 and a product of 2880.