Use the Euclidean Algorithm to Find
(A)$\operatorname { gcd } ( 203,101 )$

Question

Use the Euclidean Algorithm to Find 
(A)$\operatorname { gcd } ( 203,101 )$

Examlex · Accepted Answer

The Answer is (a) We have

203 = 2 \cdot 101 + 1

and

101 = 101 \cdot 1

. It follows that

\operatorname { gcd } ( 203,101 ) = 1

.
(b) We have

34 = 1 \cdot 21 + 13,21 = 1 \cdot 13 + 8,13 = 1 \cdot 8 + 5,8 = 1 \cdot 5 + 3,5 = 1 \cdot 3 + 2,3 = 1 \cdot 2 + 1

,

2 = 2 \cdot 1

Hence

\operatorname { gcd } ( 34,21 ) = 1

.

Use the Euclidean Algorithm to Find
(A) $\operatorname { gcd } ( 203,101 )$