Template:GCD/doc

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This template employs intricate features of template syntax.

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The {{GCD}} mathematical function template returns the greatest common divisor (GCD) of one or two integers, as a nonnegative integer, unless the templates/parser functions nesting limit (depending on the configuration settings of the MediaWiki server) is exceeded by the Euclidean algorithm, in which case an error message is returned.

$\scriptstyle \gcd(0),\,\gcd(0,\,0),\,\gcd(0,\,0,\,0),\,\dots$ are generally defined as 0. Essentially 0 acts as the top element ($\top$ or $\infty$) in this and other contexts.

Currently, the OEIS Wiki server seems to be configured to limit the number of nested template transclusions to 14 (which gives a limit of 13 iterations of the Euclidean algorithm, the {{GCD}} shell function doing only data validation and preparation for the {{~GCD}} core function, which implements the 0 th iteration of the Euclidean algorithm).

Usage

{{GCD|an integer|an integer}}

or

{{gcd|an integer|an integer}}

or

{{GCD|an integer}}

or

{{gcd|an integer}}

Valid input

One or two integers as arguments.

Examples

Examples with valid input (returns GCD, unless the 10 iterations limit of the Euclidean algorithm is exceeded, where 0 is returned)

code	result
{{GCD|0}}	0
{{GCD|0|0}}	0
{{GCD|1}}	1
{{GCD|6}}	6
{{GCD|0|6}}	6
{{GCD|6|0}}	6
{{GCD|16|6}}	2
{{GCD|16|32}}	16
{{GCD|25|625}}	25
{{GCD|544|119}}	17
{{GCD|119|544}}	17
{{GCD|-544|119}}	17
{{GCD|544|-119}}	17
{{GCD|-544|-119}}	17
{{GCD|2089|3571}}	1
{{GCD|3571|2089}}	1
{{GCD|{{Fibonacci|12}}|{{Fibonacci|11}}}} = {{GCD|144|89}}	1
{{GCD|{{Fibonacci|13}}|{{Fibonacci|12}}}} = {{GCD|233|144}}	1
{{GCD|{{Fibonacci|14}}|{{Fibonacci|13}}}} = {{GCD|377|233}}	1
{{GCD|{{Fibonacci|15}}|{{Fibonacci|14}}}} = {{GCD|610|377}}	1
{{GCD|{{Fibonacci|16}}|{{Fibonacci|15}}}} = {{GCD|987|610}}
{{GCD|{{Fibonacci|17}}|{{Fibonacci|16}}}} = {{GCD|1597|987}}
{{GCD|{{Fibonacci|18}}|{{Fibonacci|17}}}} = {{GCD|2584|1597}}
{{GCD|{{Fibonacci|19}}|{{Fibonacci|18}}}} = {{GCD|4181|2584}}
{{GCD|{{Fibonacci|20}}|{{Fibonacci|19}}}} = {{GCD|6765|4181}}
{{GCD|20891|35713}}	1
{{GCD|{{expr|2*3*5*7*11*13*17*19}}|{{expr|7*17*101*113}}}}	119
{{mpf|{{GCD|{{expr|2*3*5*7*11*13*17*19}}|{{expr|7*17*101*113}}}}}}	7^1 * 17^1

Examples with invalid input (returns an error message)

code	result
{{GCD}}
{{GCD|ten|fifteen}}
{{GCD|6.74|9}}
{{GCD|2/3|4/9}}

Code

• Template:GCD/test#Code

Test

• Template:GCD/test

See also

• {{GCD}} or {{gcd}}
• {{LCM}} or {{lcm}}