Brush her twice a day and remove the loose fur! I have a short-haired orange tabby - same problem! The brushing has solved the problem for the most part! There's still some shedding, but not nearly as much!

For shorthaired breeds, use a short-bristled, slightly stiff brush that won't irritate the skin, or use a comb with close, small teeth. Brush or comb your cat every three to four days.

Some cats shed more, some less, it all deoends and varies from cat to cat. If you are finding the grey is coughing up hairballs you could change their diet to a hairball formula diet, available through brands like Hills.
The only other way is by brushing him more, a daily brush would be best. Are you going through a seasonal change? That also affects the amount they shed.
Is he under any stress? That also affects the amount they shed. There are ...

Some cats shed more, some less, it all deoends and varies from cat to cat. If you are finding the grey is coughing up hairballs you could change their diet to a hairball formula diet, available through brands like Hills.
The only other way is by brushing him more, a daily brush would be best. Are you going through a seasonal change? That also affects the amount they shed.
Is he under any stress? That also affects the amount they shed. There are other causes, viral, dietary (when the diet is not balanced correctly). If kitty's healthy, viral would not be the cause.

As for brushing, use a compact brush not a wide-toothed one, and also use a shedding tool for cats. A shedding tool is a stainless steel comb with blades that remove dead hair from the cat’s undercoat.