(a) List all the divisors (factors) of 48 . (b) List all the divisors (factors) of 54 . (c) Use parts (a) and (b) to find the largest common divisor of 48 and 54 . (a) The divisors of 48 are \( \square \). (Simplify your answer. Use a comma to separate answers as needed.)

1. First, factorize 48 as \[ 48 = 2^4 \times 3. \] 2. To list all divisors of 48, consider all products of the factors where the exponent of 2 ranges from 0 to 4 and the exponent of 3 ranges from 0 to 1: - For the exponent of 2 equal to 0 and the exponent of 3 equal to 0: \(2^0 \times 3^0 = 1\). - For the exponent of 2 equal to 1 and the exponent of 3 equal to 0: \(2^1 \times 3^0 = 2\). - For the exponent of 2 equal to 0 and the exponent of 3 equal to 1: \(2^0 \times 3^1 = 3\). - For the exponent of 2 equal to 2 and the exponent of 3 equal to 0: \(2^2 \times 3^0 = 4\). - For the exponent of 2 equal to 1 and the exponent of 3 equal to 1: \(2^1 \times 3^1 = 6\). - For the exponent of 2 equal to 3 and the exponent of 3 equal to 0: \(2^3 \times 3^0 = 8\). - For the exponent of 2 equal to 2 and the exponent of 3 equal to 1: \(2^2 \times 3^1 = 12\). - For the exponent of 2 equal to 4 and the exponent of 3 equal to 0: \(2^4 \times 3^0 = 16\). - For the exponent of 2 equal to 3 and the exponent of 3 equal to 1: \(2^3 \times 3^1 = 24\). - For the exponent of 2 equal to 4 and the exponent of 3 equal to 1: \(2^4 \times 3^1 = 48\). 3. Hence, the divisors of 48 are \[ 1, 2, 3, 4, 6, 8, 12, 16, 24, 48. \]