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Greatest Common Divisors

Let $ a$ and $ b$ be two integers. The greatest common divisor of $ a$ and $ b$ is the biggest number that divides both of them. We denote it by ``$ \gcd(a,b)$''. Thus,

Definition 2.1  

$\displaystyle \gcd(a,b)=\max\{d : d \mid a$ and $\displaystyle d\mid b\}.$



Warning: We define $ \gcd(0,0)=0$, instead of ``infinity''.

Here are a few gcd's:

$\displaystyle \gcd(1,2)=1,\quad \gcd(0,a)=\gcd(a,0)=a, \quad\gcd(3,27)=3, \quad\gcd(2261,1275)=?$



Warning: In Davenport's book, he denotes our $ \gcd$ by HCF and calls it the ``highest common factor''. I will use the notation $ \gcd$ because it is much more common.


Subsections
William A Stein 2001-09-14