The Euclidean algorithm is an efficient and simple way to find the GCD (greatest common divisor) for two integers different from zero. It has vast ...

The Euclidean algorithm is an efficient and simple way to find the GCD (greatest common divisor) for two integers different from zero. It has vast application in various areas and is used in many important applications, such as the RSA public key cryptography method. Regarding this algorithm, choose the correct alternative:

A. The Euclidean algorithm is an efficient and simple way to find the GCD for two integers different from zero through factorization.
B. The central point of the Euclidean algorithm is the realization that a GCD can be calculated recursively. The remainder of the division in the first entry is used in the next step, until the quotient of some division results in 1.
C. Let x and y be the values for which we want to calculate their GCD and r the remainder of the division of x by y, then the formulation of the Euclidean algorithm is: gcd(x,y) = gcd(r,x).
D. Let x and y be the values for which we want to calculate their GCD and if gcd(x,y)=1 we say that x and y are multiples of each other.
E. One of the realizations that contributed to the Euclidean algorithm is that if an integer d divides x, and d divides y, then d also divides the sum of x and y and also the subtraction between them.