Question

what is Euclid's algorithm..?​

Answer 1

Answer:

the Euclid's algorithm, is an efficient method for computing the greatest common divisor of 2 integers (numbers), the largest number that divides them both without a remainder.

Answer 2

Answer:::::::::::::: """" :::::::::::::::Explanation

DEFINITION OF EUCLID'S ALGORITHM..

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Euclidean algorithm, or Euclid's algorithm, is an efficient method for computing the greatest common divisor of two integers, the largest number that divides them both without a remainder. It is named after the ancient Greek mathematician Euclid, who first described it in his Elements.

ITS FORMULA ...

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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 DO YOU PROVE IT...

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Proof. The Euclidean Algorithm proceeds by finding a sequence of remainders, r1, r2, r3, and so on, until one of them is the gcd. We prove by induction that each ri is a linear combination of a and b. It is most convenient to assume a>b and let r0=a and r1=b.

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