What is best cooler for A10-6800K (fm2) processor (atx case)

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Well that depends on your budget and what you're doing with it. The most widely recommended is the CM Hyper 212 Evo because it offers great cooling performance for the price. There are a lot of other choices however, including silent coolers, closed loop coolers, and more. You don't need a $150 closed loop cooler if you're not overclocking, but a cheaper one like a refurbished H60 is great for some overclocking, and is very quiet. Zalman also offers a lot of very nice air coolers, in all price ranges, a lot are almost silent. I encourage you to go onto a site like Newegg and use the filters there to sort through air/water coolers, decide which you want, look at which ones look nice to you, sort by price, noise, etc.
If you're not...
Well that depends on your budget and what you're doing with it. The most widely recommended is the CM Hyper 212 Evo because it offers great cooling performance for the price. There are a lot of other choices however, including silent coolers, closed loop coolers, and more. You don't need a $150 closed loop cooler if you're not overclocking, but a cheaper one like a refurbished H60 is great for some overclocking, and is very quiet. Zalman also offers a lot of very nice air coolers, in all price ranges, a lot are almost silent. I encourage you to go onto a site like Newegg and use the filters there to sort through air/water coolers, decide which you want, look at which ones look nice to you, sort by price, noise, etc.
If you're not overclocking, just about any cooler will be a large improvement over the stock, and unless your case is terribly dirty, with poor wire management, you will get perfectly safe temperatures.
 
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