I am building a PC right now, the processor I have, Intel E7400, is the retail box, so it comes with a cooling fan. There wasn't any thermal paste in the box, however, the cooling fan base has 3 grey strips of something (thermal tape?). I just want to make sure whether or not I need any thermal paste or if those 3 strips are thermal tape. Thank you.
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No you don't, the pre-applied thermalpaste will do fine.
Those three strips are thermal tape. You do not need more thermal compound.
If you plan on overclocking, however, you will need a better heatsink.