The greatest common divisor (GCD) of 24 and 49 in Q[sqrt(3)] is 1.
To find the GCD of two numbers in Q[sqrt(3)], you can use the Euclidean algorithm. First, express the numbers in terms of their prime factorization. Then, divide the larger number by the smaller number and take the remainder. Continue this process until the remainder is 0. The last non-zero remainder is the GCD.
No, the GCD of two numbers in Q[sqrt(3)] will always be a real number. This is because Q[sqrt(3)] is a subset of the real numbers.
Q[sqrt(3)] is the field of numbers that can be expressed as a + b*sqrt(3), where a and b are rational numbers. It is a subset of the complex numbers.
Yes, the GCD of two numbers in Q[sqrt(3)] can be negative. This is because the GCD is defined as the largest positive number that divides both numbers without a remainder. Therefore, the GCD can be negative if the two numbers have opposite signs.