HallsofIvy said:No, not "as desired". What you "desire" is the greatest common divisor. Saying that d^2 is a common divisor does not mean it is the GREATEST common divisor.
A greatest common divisor (GCD) is the largest positive integer that divides evenly into two or more given integers. It is also known as the greatest common factor (GCF) or highest common factor (HCF).
The most common method to find the GCD of two numbers is by using the Euclidean algorithm. This involves repeatedly dividing the larger number by the smaller number until the remainder is 0. The last non-zero remainder is the GCD.
Prime numbers are integers that are only divisible by 1 and themselves. The GCD of two prime numbers is always 1 because they do not have any common factors other than 1.
GCD is used in simplifying fractions, finding the least common multiple (LCM), and solving linear Diophantine equations. It is also used in cryptography and computer algorithms.
No, the GCD is always a positive integer by definition. However, if one or both of the numbers are negative, the GCD will remain the same as if they were positive.