Call your method in Button click event

    
<?xml version="1.0" encoding="UTF-8"?>
<mx:Application xmlns:mx="http://www.adobe.com/2006/mxml">
    <mx:Script>
    
    private function calculateFactorial(n:String):String
    {
        var y:Number=1;
        for (var x:Number = 1;x <= Number(n); x++) {
            y = y * x;
        }
        return String(y);
    }
  
    </mx:Script>
    <mx:Panel title="Calculate Factorial">
        <mx:HBox>
            <mx:Label text="Input:"/>
            <mx:TextInput id="textArea1" text="1"/>
            <mx:Button id="button1" label="Calculate" click="result.text=calculateFactorial(textArea1.text)"/>
        </mx:HBox>
        <mx:HBox>
            <mx:Label text="Factorial:"/>
            <mx:Label id="result"/>
        </mx:HBox>
    </mx:Panel>
</mx:Application>

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Call your method in Button click event : Button « Components « Flex

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