**Answer:**

**(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:

<em> Given integers </em><em>, find </em><em />

Here is an outline of the steps:

- Let , .
- Given , use the division algorithm to write .
- If , stop and output ; this is the gcd of .
- If , replace by . Go to step 2.

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 .