Easy way 2

Get the sha256 hash of the Bitcoin Core release you downloaded. On Linux, you can run, for example, sha256sum bitcoin-0.13.0-x86_64-linux-gnu.tar.gz. On Windows you can run (at a command prompt) certUtil -hashfile bitcoin-0.13.0-win32.zip SHA256. On Mac OS X, you can run shasum -a 256 bitcoin-0.13.0-osx.dmg.