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 .
