# Questions tagged [euclidean-algorithm]

For questions about the uses of the Euclidean algorithm, Extended Euclidean algorithm, and related algorithms in integers, polynomials, or general Euclidean domains. This is **not** about Euclidean geometry.

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### Canonical unit multiples in $\Bbb Z/n\Bbb Z$

I'm writing code to do computation in algebraic number fields and am (re)-learning some algebra in the process. When working with a ring, it seems useful to have an operation that "canonicalizes&...
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### Given $a$ in $\gcd(a,b)$ with $a > b > 0$, how can I find $b$ which give the maximum number of steps for the Euclidean algorithm?

Given $a$, where $a$ and $b$ are positive integers with $a > b$, how can I find the values for $b$ which give the maximum number of steps for the Euclidean algorithm $\gcd(a,b)$? For example, where ...
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I'm still learning the Euclidean algorithm and am hoping that someone can check my work on this problem: Find $gcd(1001, 11)$ $1001 = 91(11) + 0 = 90(11) + 11$ $gcd(1001, 11) = 11$