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//Title of this code
//Rextester.Program.Main is the entry point for your code. Don't change it.

using System;
using System.Collections.Generic;
using System.Linq;
using System.Text.RegularExpressions;
using System.ComponentModel;
using System.Threading;
using System.Runtime.Remoting.Messaging;

namespace Rextester
{
    public class Program
    {
        public static void Main(string[] args)
        {
            bool exited = false;
            long number = 111111111;
            
            var primes = new AsyncPrimeFactoring();
            primes.MyTaskCompleted += (a, b) =>
            {
                (a as AsyncPrimeFactoring).Result.ForEach(f => Console.WriteLine(f));
                exited = true;
            };
            primes.MyTaskAsync(number);
            
            //just so to see the output
            while(!exited)
            {
                Console.WriteLine("Doing some work on the same thread");
                Thread.Sleep(100);
            }
        }
    }
        
    public class AsyncPrimeFactoring
    {
        public List<long > Result = new List<long>();        
        void MyTask(long number)
        {
            for(long i=1; i<number; i++)
                if(number % i == 0 && IsPrime(i))
                    Result.Add(i);
        }
        bool IsPrime(long number)
        {
            if(number == 1)
                return false;
            if(number == 2 || number == 3)
                return true;
            
            for(long i=2; i<=Math.Sqrt((double)number); i++)
                if(number%i == 0)
                    return false;
                
            return true;
        }

delegate void MyTaskDelegate(long number);
        bool _myTaskIsRunning = false;
        public bool IsBusy
        {
            get { return _myTaskIsRunning; }
        }
        readonly object _sync = new object();
        
        public event AsyncCompletedEventHandler MyTaskCompleted;        
        public void MyTaskAsync(long number)
        {
            MyTaskDelegate worker = new MyTaskDelegate(MyTask);
            AsyncCallback completedCallback = new AsyncCallback(MyTaskCompletedCallback);
            
            lock (_sync)
            {
                if (_myTaskIsRunning)
                    throw new InvalidOperationException("This thread is already busy.");
                
                AsyncOperation async = AsyncOperationManager.CreateOperation(null);
                worker.BeginInvoke(number, completedCallback, async);
                _myTaskIsRunning = true;
            }
        }

void MyTaskCompletedCallback(IAsyncResult ar)
        {
            // get the original worker delegate and the AsyncOperation instance
            MyTaskDelegate worker = (MyTaskDelegate)((AsyncResult)ar).AsyncDelegate;
            AsyncOperation async = (AsyncOperation)ar.AsyncState;
            
            // finish the asynchronous operation
            worker.EndInvoke(ar);
            
            // clear the running task flag
            lock (_sync)
            {
                _myTaskIsRunning = false;
            }
            
            // raise the completed event
            AsyncCompletedEventArgs completedArgs = new AsyncCompletedEventArgs(null, false, null);
            async.PostOperationCompleted(f => OnMyTaskCompleted((AsyncCompletedEventArgs)f), completedArgs);
        }

protected virtual void OnMyTaskCompleted(AsyncCompletedEventArgs e)
        {
            if (MyTaskCompleted != null)
                MyTaskCompleted(this, e);
        }
    }
}

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Compilation time: 0.11 sec, absolute running time: 1.2 sec, cpu time: 1.11 sec, average memory usage: 20 Mb, average nr of threads: 8