Help with Factor Groups/Quotient Groups

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so factor groups/quotient groups have been tripping me up recently and if i could a definition and maybe an example from you guys that would help me out a lot.
 
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What exactly are you having trouble with? See here: http://en.wikipedia.org/wiki/Quotient_group (definition and examples as you scroll down).

I always think about the integers modulo n, under addition, as an example.
 
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