How does Euclids algorithm work?

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How does Euclids algorithm work?

The Euclidean algorithm is based on the principle that the greatest common divisor of two numbers does not change if the larger number is replaced by its difference with the smaller number. When that occurs, they are the GCD of the original two numbers.

What is Euclidean algorithm in cryptography?

The Euclidean algorithm is an efficient method to compute the greatest common divisor (gcd) of two integers. We write gcd(a, b) = d to mean that d is the largest number that will divide both a and b . If gcd(a, b) = 1 then we say that a and b are coprime or relatively prime .

How do you solve an extended Euclidean algorithm?

The extended Euclidean algorithm

  1. Set the value of the variable c to the larger of the two values a and b , and set d to the smaller of a and b .
  2. Find the quotient and the remainder when c is divided by d .
  3. If r = 0, then gcd( a , b ) = d .
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How do you find the GCF using Euclidean algorithms?

How to Find the GCF Using Euclid’s Algorithm

  1. Given two whole numbers where a is greater than b, do the division a ÷ b = c with remainder R.
  2. Replace a with b, replace b with R and repeat the division.
  3. Repeat step 2 until R=0.
  4. When R=0, the divisor, b, in the last equation is the greatest common factor, GCF.

How do you solve an extended Euclidean Algorithm?

How do you find the GCD of two numbers using Euclidean algorithm?

Recall that the Greatest Common Divisor (GCD) of two integers A and B is the largest integer that divides both A and B. The Euclidean Algorithm is a technique for quickly finding the GCD of two integers….Proof that the GCD(B,C) evenly divides A

  1. B+C=A.
  2. M⋅GCD(B,C) + N⋅GCD(B,C) = A.
  3. (M + N)⋅GCD(B,C) = A.

How do you solve GCD problems?

How to Find the Greatest Common Divisor Using LCM Method?

  1. Step 1: Determine the product of a and b.
  2. Step 2: Now, 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).
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