# CFLib.org – Common Function Library Project

## GCD(int1, int2[, showWork])

##### Last updated November 08, 2001

Version: 1 | Requires: CF5 | Library: MathLib

Description:
Calculates the GCD (greatest common factor [divisor]) of two positive integers using the Euclidean Algorithm. Optionally displays all of the steps in the calculation.

Return Values:
Returns a numeric value. Optionally outputs a string.

Example:

``````<CFSET x=13>
<CFSET y=130>

<cfoutput>
Given:<BR>
x=#x#<BR>
y=#y#<BR>
G.C.D. = #GCD(x,y,"yes")#
</cfoutput>
``````

Parameters:

Name Description Required
int1 Positive integer. Yes
int2 Positive integer. Yes
showWork Boolean. Yes or No. Specifies whether to display work. Default is No. No

Full UDF Source:

``````/**
* Calculates the GCD (greatest common factor [divisor]) of two positive integers using the Euclidean Algorithm.
*
* @param int1      Positive integer.
* @param int2      Positive integer.
* @param showWork      Boolean.  Yes or No.  Specifies whether to display work.  Default is No.
* @return Returns a numeric value.  Optionally outputs a string.
* @author Shakti Shrivastava (shakti@colony1.net)
* @version 1, November 8, 2001
*/
function GCD(int1, int2)
{
Var ShowWork=False;
If (ArrayLen(Arguments) eq 3 AND Arguments eq "yes"){
ShowWork=True;
}

// if both numbers are 0 return undefined
if (int1 eq 0 and int2 eq 0) return 'Undefined';

// if both numbers are equal or either one of them is equal to 0
// then return any 1 of those numbers appropriately
if (int1 eq int2 or int2 eq 0) return int1;
if (int1 eq 0) return int2;

// if int2 divides int1 "properly" then we have reached our final
//   step. So we output the last step and exit the function.
if (int1 mod int2 eq 0) {
if(ShowWork EQ True) {
WriteOutput("<br>"&int1&"= "&fix(int1/int2)&" X "&int2&" + "&int1 mod int2);
}
// this line outputs the last iteration
if (ShowWork EQ True) {
return "<p>GCD = "&int2; //print the GCD
}
else{
return int2;
}
}

// if int2 does not divides int1 "properly" then we recurse using
// int1 equal to int2 and int2 equal to int1 mod int2
else {
if(ShowWork EQ True)
// this line outputs calculations from each iteration. you can safely
// delete/comment out this line if you dont need to display the steps.
WriteOutput("<br>"&int1&"= "&fix(int1/int2)&" X "&int2&" + "&int1 mod int2);
}
//since we still have not reached the last step we recall the function
//(recurse)
GCD(int2, int1 mod int2, ShowWork);
}
``````

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