Question

Apply Euclid’s algorithm to find the GCD (Greatest Common Divisor) of 126 and 28.

Describe or give the pseudocode of the consecutive integer checking algorithm for finding the GCD. What is the time complexity of this second algorithm? Explain.

Answer 1

Euclid Algoithm:

int gcd(int m, int n)

{

    if (m % n == 0)

        return n;

    return gcd(n, m % n);

}

m = 126

n = 28

gcd( 126, 28 )

Here, ( 126 % 28 = 14 ) != 0.

So, again recursively call gcd( 28 , 126 % 28 ) = gcd( 28, 14 )

gcd( 28, 14 )

Here, ( 28 % 14 = 0 ) == 0.

So, it returns 14.

Hence, gcd = 14.

pseudocode of the consecutive integer checking algorithm:

Let a, b be the two numbers

1. ​Set T with the smaller value among {a,b}. So, T = min(a, b)
2. Find the value of m % T. If the output is not 0, then we move to 4, otherwise we move to 3.
3. Find the value of n % T. If the output is not 0, then we move to 4, otherwise we get the ans as t and the algorithm is terminated.
4. The value of T is decremented by 1.

T = T - 1