\( \operatorname { MCD } ( 40,64,104 \)

To find the greatest common divisor (GCD), also known as the maximum common divisor (MCD), of the numbers 40, 64, and 104, we can use the prime factorization method. 1. **Prime factorization of each number:** - **40:** \[ 40 = 2^3 \times 5^1 \] - **64:** \[ 64 = 2^6 \] - **104:** \[ 104 = 2^3 \times 13^1 \] 2. **Identify the common prime factors:** The only common prime factor among the three numbers is \(2\). 3. **Determine the minimum exponent for the common prime factor:** - For \(2\): - In 40, the exponent is 3. - In 64, the exponent is 6. - In 104, the exponent is 3. - The minimum exponent is \(3\). 4. **Calculate the GCD:** \[ \text{GCD} = 2^{\text{min}(3, 6, 3)} = 2^3 = 8 \] Thus, the greatest common divisor (MCD) of 40, 64, and 104 is \(\boxed{8}\).