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The administrative distance of a default route is 1 (one) and is seen as a static route.
by default the administrative distance is one (1), but you can give it an optional value. The metric is zero (0).
default
The route via Path B is installed because the EIGRP route has the best metric to network 10.2.0.0/16. The route via Path A is installed because the static route has the best metric to network 10.2.0.0/16. The route via Path B is installed because the EIGRP route has the lowest administrative distance to network 10.2.0.0/16. The route via Path A is installed because the static route has the lowest administrative distance to network 10.2.0.0/16.
default-information originate
This is where administrative distance comes into play. The lowest one gets used in the routing table. A static route always has a lower AD than dynamic routing processes. So the static route will be used.
A Admin can set the Administrative Distance (AD) on a static route to tell the router how reliable the route is. Dynamic routing protocols use metrics to determine route reliability.
router(config)#ip route 0.0.0.0 0.0.0.0 10.1.1.1
R1# show ip route
the default gateway is the most common static route used in a host computer. netstat -r is the command line command to obtain the routing table.
Compared to RIP, EIGRP has a lower administrative distance.
Administrative distance refers to the trustworthiness of a particular route. Routes with the smallest metric to a destination indicate the best path.