The cut factor is actually exactly related to the size of your camera's sensor. Since 35mm has become a standard in film cameras, full frame "Full Frame" corresponds to 35mm in the digital cameras we are using now.
Calculation of Crop Factor:
Calculating the crop factor is pretty easy. If you know the physical size of the crop sensor, find the diagonals of both sensors using the Pythagorean Theorem (a² + b² = c²), then divide the diagonal of the full-frame sensor by the diagonal of the crop sensor.
For example, if you take a photo with a full frame Sony A900, you will get a black framed image like the one below, but if you take the same photo with my Sony A55 (with 1.5x crop factor), you will see the red framed area because the sensor is not full frame. If you're using a full-frame camera, there's no need to mention the cut-off factor, so it's the focal length of your lens, but if you're not using a full-frame camera, your sensor will have a multiplier depending on its size.
For instance; When we use the Minolta 70-210mm F/4 lens with the Sony A900 camera, there will be no crop factor, but I have to do a few mathematical operations to find the effective focal length that I will use the same lens with on my 1.5 factor Sony A55. (70mmx1.5=105mm) and (210mmx1.5=305mm). As a result, when we use a camera with a cut factor of 1.5, a 70-210mm lens appears as if it were a 105-305mm lens.
Crop factors used in cameras
Sony – Full frame sensor (24x36mm) – A900, A850, A99(future) – APS-C sensor = 1.5x “Crop Factor” (23.5 x 15.6 mm ) – A77, A65, A57, A55, A35, A37, Nex-7, Nex-5n, Nex-3C
Canon – Full-frame Sensor (~ 36 x 24mm) – 5D, 5D Mark II, EOS-1Ds Mark III – APS-H sensor = 1.3x “Cut Factor” (~ 29 x 19mm) – EOS-1D Mark IV – APS-C sensor = 1.6x “Cut Factor” (~ 22 x 15mm) – Canon 50D, 40D, Rebel XSI
Nikon – FX sensor = Full Frame (~ 23.9 x 36mm) – D3X, D3S, D3, D700 – DX sensor = 1.5x “Cut Factor” (~ 15.8 x 23.6mm) – D90, D300S