Hello @alfredgupton641 ,
EIGRP uses a composite metric that is cumulative on delay ( it sums up all the delays of outgoing interfaces of routers on the path) and inversely proportional to the lowest bandwidth link on the path.
EIGRP metric is a 32 bit integer in classic implementation
named EIGRP newest implementation uses 64 bit integer to be able to deal with 40 GE and above links.
A scale factor is used to resize the 64 bit metric into a 32 bit value to provide it to the IP routing table manager that uses 32 bit integers for metric values
>> Does EIGRP use bandwidth while OSPF uses priority?
No OSPF priority is not part of metric computation but it is used for OSPF DR / BDR election in a LAN segment
>> Does EIGRP uses delay while OSPF uses COST?
EIGRP uses cumulative delay on path AND lowest bandwidth on path as explained above OSPF uses cumulative cost on links. Cisco uses an auto-reference bandwidth ( default value is 100 Mbps) that is used to assign a cost to each OSPF interface. All OSPF routers must use te same value that has to be provided in Mbps.
>> Does both OSPF and EIGRP use delay?
No only EIGRP uses delay
>> Does EIGRP use hop count while OSPF uses bandwidth?
No, EIGRP does not use hop count in the composite metric calculation, however it keeps trace of hop count .
MAx hop count default is 100.
>> Both OSPF and EIGRP have mechanisms to reduce the size of the routing tables.
True
>> Does both OSPF and EIGRP use summarization and zones/areas?
OSPF can summarize internal routes at area boundaries on ABR nodes.
EIGRP has no zone concept as far as I know
>> Does EIGRP uses variance while OSPF uses summarization?
No !!!!!!! Variance is used in EIGRP to support un equal cost multi path load sharing but all selected paths must pass the Feasbiity condition . Variance and router summarization are different concepts
>> Does EIGRP uses summarization while OSPF uses areas?
No !!!!!!!
EIGRP can summarize out of a specific interface with some caveats. OSPF can summarize only at area boundary as explained above
>> EIGRP uses zones while OSPF uses areas?
No !!!!!!!
EIGRP does not use zones as far as I know , OSPF uses multiple areas for increased scalability
You need to study a little more your questions show that you are missing most of the basic concepts.
Hope to help
Giuseppe
