General Electric agreed on Monday to sell its biopharmaceutical business to Danaher for about $21.4 billion, as the troubled industrial giant sells off divisions to pay down debt and steady its business.

In selling the business, G.E. took another big step in what has become a drastic slimming-down of an American corporate icon.

Known for decades as a titan of American business, G.E. has struggled in recent years with a bevy of problems. Under a succession of leaders, the company has announced the sale or spinoff of enormous divisions, whittling down operations like finance and energy.

Last summer, G.E. said it planned to spin off its health care division — including the biopharmaceutical unit, which sells equipment and software to biotechnology companies — and sell its stake in a big oil field services business, Baker Hughes.