Use the Euclidean algorithm to find
(a) $\operatorname { gcd } ( 203,101 )$.
(b) $\operatorname { gcd } ( 34,21 )$.

Name: Use the Euclidean algorithm to find (a) $\operatorname { gcd } ( 203,101 )$. (b) $\operatorname { gcd } ( 34,21 )$.
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Question

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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) gcd⁡(203,101)\operatorname { gcd } ( 203,101 )gcd(203,101)

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