Convert RGB color to CMYK?

Question

I'm looking for an algorithm to convert an RGB color to CMYK. Photoshop is performing the conversion below:

R = 220 G = 233 B = 174

C = 15 M = 0 Y = 40 K = 0

Answer 1

I agree with the previous answers, but I want to say that:

if ( K == 1 ) 
{ 
   C = 0
   M = 0
   Y = 0
} 

It can be if r = g = b = 0.

Answer 2

Check out this link: http://www.codeproject.com/KB/applications/xcmyk.aspx. It gives this formula.

Black   = minimum(1-Red,1-Green,1-Blue)
Cyan    = (1-Red-Black)/(1-Black)
Magenta = (1-Green-Black)/(1-Black)
Yellow  = (1-Blue-Black)/(1-Black) 

Answer 3

My complete example for C# conversion between CMYK <-> HEX:

public class ColorConverter
{
    public static string CMYKtoHex(decimal[] cmyk)
    {
        if (cmyk.Length != 4) return null;

        var r = (int)(255 * (1 - cmyk[0]) * (1 - cmyk[3]));
        var g = (int)(255 * (1 - cmyk[1]) * (1 - cmyk[3]));
        var b = (int)(255 * (1 - cmyk[2]) * (1 - cmyk[3]));

        var hex = "#" + r.ToString("X2") + g.ToString("X2") + b.ToString("X2");
        return hex;
    }

    public static decimal[] HexToCMYK(string hex)
    {
        decimal computedC = 0;
        decimal computedM = 0;
        decimal computedY = 0;
        decimal computedK = 0;

        hex = (hex[0] == '#') ? hex.Substring(1, 6) : hex;

        if (hex.Length != 6)
        {
            return null;
        }

        decimal r = int.Parse(hex.Substring(0, 2), System.Globalization.NumberStyles.HexNumber);
        decimal g = int.Parse(hex.Substring(2, 2), System.Globalization.NumberStyles.HexNumber);
        decimal b = int.Parse(hex.Substring(4, 2), System.Globalization.NumberStyles.HexNumber);

        // BLACK
        if (r == 0 && g == 0 && b == 0)
        {
            computedK = 1;
            return new[] { 0, 0, 0, computedK };
        }

        computedC = 1 - (r / 255);
        computedM = 1 - (g / 255);
        computedY = 1 - (b / 255);

        var minCMY = Math.Min(computedC, Math.Min(computedM, computedY));

        computedC = (computedC - minCMY) / (1 - minCMY);
        computedM = (computedM - minCMY) / (1 - minCMY);
        computedY = (computedY - minCMY) / (1 - minCMY);
        computedK = minCMY;

        return new[] { computedC, computedM, computedY, computedK };
    }
 }