If you bought a pre-built computer (HP, Dell, Lenovo, etc.) that came with Windows 7 pre-installed, you have an OEM (Original Equipment Manufacturer) license. You can usually find the product key on a sticker on the side or bottom of the computer (often called a Certificate of Authenticity).
If Windows 7 is still running on the machine, tools like ProduKey can extract the key from the registry. Common Issues and Troubleshooting can i use my windows 7 key for windows 10
Your key works with either architecture. If you bought a pre-built computer (HP, Dell, Lenovo, etc