Factor Groups

[Dawson64]

Why does it make sense ( when considering Z4)to form the factor group

Z4 / (2Z4) where kZn = {0, k mod n, 2k mod n, ..., nk mod n}?

I believe that this above factor group is isomorphic to Z2, but how can I prove this?

[Newtime]

Why does it make sense ( when considering Z4)to form the factor group

Z4 / (2Z4) where kZn = {0, k mod n, 2k mod n, ..., nk mod n}?

I believe that this above factor group is isomorphic to Z2, but how can I prove this?

The groups you're considering are of very small order so in this case, just write out the elements and remember the number of groups of order 2 is ______ . In general, based off your definition, you should be able to identify the group pretty easily by what you know about finite cyclic groups.