Examples of Euclid's algorithm for finding GCD of large numbers?

Answer 1

Euclid's algorithm is a time-tested method for finding the greatest common divisor (GCD) of two numbers. It's based on the principle that the greatest common divisor of two numbers also divides their difference. This algorithm is efficient and works well for large numbers, making it a practical choice in numerous applications.

The algorithm operates in a recursive or iterative manner, continually reducing the problem size until it reaches a base case. Here’s how Euclid's algorithm works:

print (gcd (a, b) ) # Output: 3ere >a>b , subtract b from a. Replace a with (a−b).

Repeat this process until a and b become equal, at which point, a (or b) is the GCD of the original numbers.

A more efficient version of Euclid’s algorithm, known as the Division-based Euclidean Algorithm, operates as follows:

Given two numbers a and b, where >a> b, find the remainder of a divided by b, denoted as r.

Replace a with b and b with r.

Repeat this process until b becomes zero. The non-zero remainder, a, is the GCD of the original numbers.

In this example, even though

a and b are large numbers, the algorithm quickly computes the GCD. The division-based version of Euclid’s algorithm is more efficient than the subtraction-based version, especially for large numbers, as it reduces the problem size more rapidly.

Euclid's algorithm is a fundamental algorithm in number theory, with applications in various fields including cryptography, computer science, and engineering. Its efficiency and simplicity make it a powerful tool for computing the GCD, even for large numbers.

Answer 2

Use a character array to save the large number