# Prove that the second argument to (operatorname{gcd}()) decreases by at least a factor of 2 for every

## Question:

Prove that the second argument to \(\operatorname{gcd}()\) decreases by at least a factor of 2 for every second recursive call, and then prove that \(\operatorname{gcd}(p, q)\) uses at most \(2 \log _{2} n+1\) recursive calls where \(n\) is the larger of \(p\) and \(q\).

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**Related Book For**

## Introduction To Programming In Java An Interdisciplinary Approach

**ISBN:** 9780672337840

2nd Edition

**Authors:** Robert Sedgewick, Kevin Wayne