Fixing Windows Update Error 8007000E After Windows 7 SP1 Clean Install

After a clean install of Windows 7 SP1 32-bit (I'm unsure about 64-bit), Windows Update fails with an 8007000E error.

There is information on the Microsoft website regarding this, but the suggested solutions did not work for me.

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I have found the solution, so I am leaving a note here for my own reference.

The cause seems to be that the Windows Update program is outdated, and it causes a memory error when attempting to apply a large number of patches all at once.

I found information on TechNet.

http://blogs.technet.com/b/systemcenterjp/archive/2015/09/30/3648889.aspx

In my case, the issue was resolved by installing the latest Windows Update client.

As of March 2016, the latest version can be found here:

https://support.microsoft.com/ja-jp/kb/3138612