From Latin 'planta' (sprout, sole of foot) — the factory sense came from 'planting' equipment in a location.
A living organism that grows in earth; a factory or industrial installation.
From Old English 'plante' meaning 'young tree, herb,' from Latin 'planta' meaning 'sprout, shoot, cutting,' and also 'sole of the foot.' The connection may be that you press a cutting into soil with your foot. Key roots: planta (Latin: "sprout, cutting; sole of foot").