The most common and most likely answer to this crossword clue is the 4 letter word MILL
I've seen this crossword clue in The Daily Telegraph
M
I
L
L
More clues leading to the result MILL
Buddy explains!

The straight part
We know that "Factory" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case factory = mill.The cryptic/wordplay part
In cryptic crossword there's often an wordplay/cryptic part as well.This part involves a more complex hint, such as an anagram, homophone, hidden word, etc.
Sadly, We don't have an explanation for this specific crossword clue yet.
What does MILL mean?
MILL noun- A grinding apparatus for substances such as grains, seeds, etc.
- The building housing such a grinding apparatus.
- A machine used for expelling the juice, sap, etc., from vegetable tissues by pressure, or by pressure in combination with a grinding, or cutting process.
- A machine for grinding and polishing.
- The raised or ridged edge or surface made in milling anything, such as a coin or screw.
- A manufacturing plant for paper, steel, textiles, etc.
- A building housing such a plant.
- An establishment that handles a certain type of situation or procedure routinely, or produces large quantities of an item without much regard to quality, such as a divorce mill, a puppy mill, etc.
- An institution awarding educational certificates not officially recognised
- An engine.
- A boxing match, fistfight.
- (die sinking) A hardened steel roller with a design in relief, used for imprinting a reversed copy of the design in a softer metal, such as copper.
- An excavation in rock, transverse to the workings, from which material for filling is obtained.
- A passage underground through which ore is shot.
- A milling cutter.
- A treadmill.
- A typewriter used to transcribe messages received.
- To grind or otherwise process in a mill or other machine.
- To shape, polish, dress or finish using a machine.
- To engrave one or more grooves or a pattern around the edge of (a cylindrical object such as a coin).
- (followed by around, about, etc.) To move about in an aimless fashion.
- To cause to mill, or circle around.
- (of air-breathing creatures) To swim underwater.
- (of a whale) To swim suddenly in a new direction.
- To beat; to pound.
- To pass through a fulling mill; to full, as cloth.
- To roll (steel, etc.) into bars.
- To make (drinking chocolate) frothy, as by churning.
- To undergo hulling.
- To take part in a fistfight; to box.
- To fill (a winze or interior incline) with broken ore, to be drawn out at the bottom.
- (thieves' cant) To commit burglary.
- An obsolete coin worth one thousandth of a US dollar, or one tenth of a cent.
- One thousandth part, particularly in millage rates of property tax.
- An angular mil, a unit of angular measurement equal to 1⁄6400 of a complete circle. At 1000 metres one mil subtends about one metre (0.98 m). Also 1⁄6000 and 1⁄6300 are used in other countries.
- A unit of measurement equal to 1⁄1000 of an inch, usually used for thin objects, such as sheets of plastic.
- A former subdivision (1/1000) of the Maltese lira
- (plural "mil") Abbreviation of million.
- A unit of measure of capacity, being one thousandth of a litre. Symbol: ml
- A line of three matching pieces in nine men's morris and related games.
- (trading card games) Discarding a card from one's deck.
- (trading card games) A strategy centered on depleting the opponent's deck.
- (trading card games) To move (a card) from a deck to the discard pile.
- (Hearthstone) To destroy (a card) due to having a full hand.