WASHINGTON — U.S. factory activity shrank for the third straight month in August as new orders, production and employment all fell. The report adds to other signs that manufacturing is slowing.

The Institute for Supply Management, a trade group of purchasing managers, says its index of manufacturing activity ticked down to 49.6. That’s down from 49.7 in July and the lowest reading in three years. A reading below 50 indicates contraction.

Factories have been a key source of jobs and growth since the recession ended in June 2009. But the sector has shown signs of weakness in recent months.

The report showed factories kept hiring in July but at a slower pace. And production dropped sharply to 47.2.