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>, find </em> <em />
<em />
Here is an outline of the steps:
- Let  , , . .
- Given  , use the division algorithm to write , use the division algorithm to write . .
- If  , stop and output , stop and output ; this is the gcd of ; this is the gcd of . .
- If  , replace , replace by by . Go to step 2. . 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:
 we apply the Euclidean algorithm:

The process stops since we reached 0, and we obtain  .
.
(b) To find  we apply the Euclidean algorithm:
 we apply the Euclidean algorithm:

The process stops since we reached 0, and we obtain  .
.
(c) To find  we apply the Euclidean algorithm:
 we apply the Euclidean algorithm:

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