How does Euclid algorithm calculate GCD?

Posted on by Muna Meyer

How does Euclid algorithm calculate GCD?

The Euclidean Algorithm for finding GCD(A,B) is as follows:

  1. If A = 0 then GCD(A,B)=B, since the GCD(0,B)=B, and we can stop.
  2. If B = 0 then GCD(A,B)=A, since the GCD(A,0)=A, and we can stop.
  3. Write A in quotient remainder form (A = B⋅Q + R)
  4. Find GCD(B,R) using the Euclidean Algorithm since GCD(A,B) = GCD(B,R)

What is the time complexity of GCD?

Euclid’s Algorithm: It is an efficient method for finding the GCD(Greatest Common Divisor) of two integers. The time complexity of this algorithm is O(log(min(a, b)).

How do you find the GCD?

The steps to calculate the GCD of (a, b) using the LCM method is:

  1. Step 1: Find the product of a and b.
  2. Step 2: Find the least common multiple (LCM) of a and b.
  3. Step 3: Divide the values obtained in Step 1 and Step 2.
  4. Step 4: The obtained value after division is the greatest common divisor of (a, b).

What is the GCD of 12 and 3?

The GCF of 3 and 12 is 3. To calculate the GCF (Greatest Common Factor) of 3 and 12, we need to factor each number (factors of 3 = 1, 3; factors of 12 = 1, 2, 3, 4, 6, 12) and choose the greatest factor that exactly divides both 3 and 12, i.e., 3.

How do you write GCD?

For example, the greatest common factor of 15 and 10 is 5, since both the numbers can be divided by 5.

  1. 15/5 = 3.
  2. 10/5 = 2.
  3. If a and b are two numbers then the greatest common divisor of both the numbers is denoted by gcd(a, b).
  4. Suppose, 4, 8 and 16 are three numbers.
  5. 4 → 1,2,4.
  6. 8 → 1,2,4,8.
  7. 16 → 1,2,4,8,16.

Is Euclidean algorithm polynomial time?

Very frequently, it is necessary to compute gcd(a, b) for two integers a and b. We now discuss an algorithm — the Euclidean algorithm — that can compute this in polynomial time.

What recursion is used in gcd?

In the above program, gcd() is a recursive function. It has two parameters i.e. a and b. If b is greater than 0, then a is returned to the main() function. Otherwise, the gcd() function recursively calls itself with the values b and a%b.