will these bottleneck

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If I were you I'd go for at least an i5 4570. You'll probably notice some difference in cpu intensive games between the 4440 and 4570, but not so much between a 4570 and 4670k.

If you want to save money (I'm assuming you do since you chose an i5 4440), then I'd go for a cheaper cooler to offset the extra cost of a 4570. At stock clocks even a cheap cpu cooler for $20-30 will be a massive improvement over stock.

Mattib 050

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Nov 24, 2013
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If I were you I'd go for at least an i5 4570. You'll probably notice some difference in cpu intensive games between the 4440 and 4570, but not so much between a 4570 and 4670k.

If you want to save money (I'm assuming you do since you chose an i5 4440), then I'd go for a cheaper cooler to offset the extra cost of a 4570. At stock clocks even a cheap cpu cooler for $20-30 will be a massive improvement over stock.
 
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