A home broadband router uses two IP addresses. One is the private address on the local network. The other is the external, public IP address that communicates with external networks on the internet.
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The external address managed by a router is set when it connects to the ISP with a broadband modem. This address can be viewed via web-based IP lookup services such as IP Chicken and also via the router.
It's a similar process for other manufacturers, but on Linksys routers you can see the public IP address on the Status page in the Internet section. NETGEAR routers may call this the Internet Port IP Address and display it on the Maintenance > Router Status screen.
Home routers have their local address set to a standard, private IP address number. It is usually the same address for other models from that manufacturer and can be found in the manufacturer's documentation.