What is the prefix for the factor one billionth?

The prefix that represents the factor of one billionth is "nano." In the metric system, "nano" signifies a factor of (10^{-9}), which is equivalent to one billionth. This means that one nanometer equals one billionth of a meter.

Understanding metric prefixes is essential in fields such as science and engineering, particularly in areas that require precision at microscopic or atomic levels. For instance, nanoscale technologies are utilized in various applications, including electronics and materials science.

The other prefixes, while also denoting specific factors, correspond to different magnitudes. "Milli," for instance, denotes one thousandth ((10^{-3})), and "micro" indicates one millionth ((10^{-6})). "Pico" refers to one trillionth ((10^{-12})). Each of these prefixes serves its purpose in various contexts, but none represents the factor of one billionth as accurately as "nano" does.