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Does your router have an USB port, if yes you could plug it in there and have a shared network drive. Some External HDs require more power. I think the real question is will you HD work with your Galaxy Note? http://www.youtube.com/watch?v=XndM31sH-sM
If you pull the HD from a PC to access via USB you will need this. http://www.amazon.com/Drive-Adapter-Converter-Optical-External/dp/B000YJBL78
http://www.samsung.com/us/news/20228"USB Connection Kit to allow usage of thumb drives or USB peripherals"http://www.amazon.com/Juiced-Systems-Connection-Samsung-Tablets/dp/B006MAWKRIhttp://www.ebay.com/itm/30pin-USB-Connection-Kit-OTG-HOST-CABLE-Fr-Samsung-Galaxy-Note-10-1-N8000-N8010-/251121575594
Hope this helps.