What is Euclidean algorithm example?

The Euclidean algorithm is a way to find the greatest common divisor of two positive integers, a and b. First let me show the computations for a=210 and b=45. Divide 210 by 45, and get the result 4 with remainder 30, so 210=4·45+30. Divide 45 by 30, and get the result 1 with remainder 15, so 45=1·30+15.

What is meant by Euclidean algorithm?

Definition of Euclidean algorithm



: a method of finding the greatest common divisor of two numbers by dividing the larger by the smaller, the smaller by the remainder, the first remainder by the second remainder, and so on until exact division is obtained whence the greatest common divisor is the exact divisor.

What is formula for Euclidean algorithm?

If we examine the Euclidean Algorithm we can see that it makes use of the following properties: GCD(A,0) = A. GCD(0,B) = B. If A = B⋅Q + R and B≠0 then GCD(A,B) = GCD(B,R) where Q is an integer, R is an integer between 0 and B-1.

How is Euclidean algorithm used?

Video quote: So for instance with the number 10 the number 1 divides in 10 times the number 2 divides in 5 times 3 and 4 don't divide in at all. 5 does it goes in twice.

How many steps does the Euclidean algorithm take?

2:5=1 × 3 + 2; 3:3=1 × 2 + 1; 4:2=1 × 1 + 1; 5:1=1 × 1 + 0; 1 is the GCD of 8 and 5. Even though the numbers are small it took 5 steps to find the GCD using the algorithm. The algorithm goes through all the Fibonacci numbers until it reaches 0.

Why is Euclidean algorithm important?

The Euclidean algorithm is useful for reducing a common fraction to lowest terms. For example, the algorithm will show that the GCD of 765 and 714 is 51, and therefore 765/714 = 15/14. It also has a number of uses in more advanced mathematics.

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.

How fast is Euclid’s algorithm?

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 prove Euclid’s algorithm?

Video quote: That says if we have an integer a that equals B times some quotient Q plus a remainder R. Then the GCD of a and B is the same as the GCD of B and R.

Who invented Euclid’s algorithm?

Euclid

2. Who invented Euclid’s algorithm? Explanation: Euclid invented Euclid’s algorithm.