Use the Euclidean Algorithm to compute the greatest common divisors indicated. (a) gcd(20, 12) (b) gcd(100, 36) (c) gcd(207, 496)

(a)

(b)

(c)

Step-by-step explanation:

The Euclidean algorithm is an efficient method for computing the greatest common divisor of two integers, without explicitly factoring the two integers.

The Euclidean algorithm solves the problem:

                                  Given integers , find

Here is an outline of the steps:

The division algorithm is an algorithm in which given 2 integers N and D, it computes their quotient Q and remainder R.

Let's say we have to divide N (dividend) by D (divisor). We will take the following steps:

Step 1: Subtract D from N repeatedly.

Step 2: The resulting number is known as the remainder R, and the number of times that D is subtracted is called the quotient Q.

(a) To find we apply the Euclidean algorithm:

The process stops since we reached 0, and we obtain .

(b) To find we apply the Euclidean algorithm:

The process stops since we reached 0, and we obtain .

(c) To find we apply the Euclidean algorithm:

The process stops since we reached 0, and we obtain .