Why do homes and factories have different voltages?

Factories often have three phase voltage, and higher voltage (480V) compared to homes. Three phase voltage is necessary for three phase induction motors, which are often used in factories. These are very rarely used in homes. Three phase power requires more equipment than single phase (2 or three step down Transformers vs. one for single phase).

Factories use higher than home voltages so wiring can be sized down and still provide the necessary power ( P = V*I ). Higher voltage equipment naturally costs more, and homes typically do not need the amount of power that would require excessively large guage wires, so it is more economical (and safer) to run lower voltage.