Can a 600w psu power a gtx 1070 and an i7 7700k

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Yes, even 550 watts will be enough with comfortable headroom. 450 watts could do it to as long as the unit was good but you won't be left with much headroom. Just make sure the PSU choice is decent quality, which in your case it is (the SF600w is a great quality unit).
Yes, even 550 watts will be enough with comfortable headroom. 450 watts could do it to as long as the unit was good but you won't be left with much headroom. Just make sure the PSU choice is decent quality, which in your case it is (the SF600w is a great quality unit).
 
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