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I have taken out the drive from my computer and put it in an USB-drive. The size of the partition is 488GB and I have copied to a virtual disk file on another USB-drive.
There is another 2 TB free space on this new drive.
The search is done on another computer with the search directed to the E drive. There is 340 GB free on the C-drive.
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How big memory is needed to be able to not have the "not enough memory available" coming up?
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Please note that memory and hard drive space are two entirely different things; they happen to share the same units of measurement (KB/MB/GB/TB/etc), but perform entirely different tasks for your computer.
However, I notice that you're running Recuva on a 32-bit version of Windows. Please note that Recuva can only operate in a very limited manner on 32-bit versions because they can only access about 3.6GB of memory at the most (you have 2GB according to the screenshot); in fact, it's actually a little bit of a surprise that it didn't crash outright instead of giving you that message.
(I believe this includes 'virtual memory', i.e. space set aside on your hard drive for extra data to be saved to.)
Unfortunately, because of that, the best recommendation that I can give is to use a computer with a 64-bit version of Windows, preferably with more memory. Alternately, you may wish to have a reputable recovery service take a look at the drive instead, as they would certainly have the needed equipment.