What İs Euclidean Algorithm ?

Question

Show With Examples

Answer 1

both A and B.

The Euclidean Algorithm is a technique for quickly finding the GCD of two integers.

The Algorithm

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

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

Example:

Find the GCD of 270 and 192

A=270, B=192A ≠0B ≠0Use long division to find that 270/192 = 1 with a remainder of 78. We can write this as: 270 = 192 * 1 +78Find GCD(192,78), since GCD(270,192)=GCD(192,78)

A=192, B=78

A ≠0B ≠0Use long division to find that 192/78 = 2 with a remainder of 36. We can write this as:192 = 78 * 2 + 36Find GCD(78,36), since GCD(192,78)=GCD(78,36)

A=78, B=36

A ≠0B ≠0Use long division to find that 78/36 = 2 with a remainder of 6. We can write this as:78 = 36 * 2 + 6Find GCD(36,6), since GCD(78,36)=GCD(36,6)

A=36, B=6

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Answer 2

Euclidean algorithm
https://en.wikipedia.org/wiki/Euclidean_algorithm

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Answer 3

Eucledon Algorithm is a technique of quickly find the GCD(Greatest Common Divisor)of two numbers.
e.g.
gcd(a,b)
if(b==0)
return a;
else
{
return gcd(b,a%b)
}

Answer 4

I actually had no clue about this, so it is interesting to hear about it. I enjoyed reading up on it and it seems like a very useful algorithm!