Discrete Mathematics and Its Applications, Seventh Edition

Published by McGraw-Hill Education
ISBN 10: 0073383090
ISBN 13: 978-0-07338-309-5

Chapter 5 - Section 5.4 - Recursive Algorithms - Exercises - Page 370: 4

Answer

$\gcd(12, 17) = 1$

Work Step by Step

With the given input, the algorithm uses the else clause to find that $$\gcd(12, 17) = \gcd(17 \mod 12, 12) = \gcd(5, 12)$$ It uses this clause again to find that $$\gcd(5, 12) = \gcd(12 \mod 5, 5) = \gcd(2, 5)$$, then to get $$\gcd(2, 5) = \gcd(5 \mod 2, 2) = \gcd(1, 2)$$, then $$\gcd(1, 2) = \gcd(2 \mod 1, 1) = \gcd(0, 1)$$, Finally, to find $\gcd(0, 1)$ it uses the first step with a = 0 to find that $\gcd(0, 1) = 1$. Consequently, the algorithm finds that $\gcd(12, 17) = 1$.
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