Why do we always divide RGB values by 255?

RGB (Red, Green, Blue) are 8 bit each.
The range for each individual colour is 0-255 (as 2^8 = 256 possibilities).
The combination range is 256*256*256.

By dividing by 255, the 0-255 range can be described with a 0.0-1.0 range where 0.0 means 0 (0x00) and 1.0 means 255 (0xFF).

RGB values are usually stored as integers to save memory. But doing math on colors is usually done in float because it's easier, more powerful, and more precise. The act of converting floats to integers is called "Quantization", and it throws away precision.

Typically, RGB values are encoded as 8-bit integers, which range from 0 to 255. It's an industry standard to think of 0.0f as black and 1.0f as white (max brightness). To convert [0, 255] to [0.0f, 1.0f] all you have to do is divide by 255.0f.

If you care, this is the formula to convert back to integer: (int)floor(x * 255.0f + 0.5f). But first clamp x to [0.0f, 1.0f] if necessary.

This is a bit of a generic question since it can be specific to the platform and even to the method. It really comes down to math and getting a value between 0-1. Since 255 is the maximum value, dividing by 255 expresses a 0-1 representation.

Each channel (Red, Green, and Blue are each channels) is 8 bits, so they are each limited to 256, in this case 255 since 0 is included. As the reference shows, systems typically use values between 0-1 when using floating point values.

http://en.wikipedia.org/wiki/RGB_color_model

See Numeric Representations.

These ranges may be quantified in several different ways: From 0 to 1, with any fractional value in between. This representation is used in theoretical analyses, and in systems that use floating point representations. Each color component value can also be written as a percentage, from 0% to 100%. In computers, the component values are often stored as integer numbers in the range 0 to 255, the range that a single 8-bit byte can offer. These are often represented as either decimal or hexadecimal numbers. High-end digital image equipment are often able to deal with larger integer ranges for each primary color, such as 0..1023 (10 bits), 0..65535 (16 bits) or even larger, by extending the 24-bits (three 8-bit values) to 32-bit, 48-bit, or 64-bit units (more or less independent from the particular computer's word size).