I need some help with these review problems I have for an upcoming final.

How many homomorphisms are there of Z onto Z?

How many homomorphisms are there of Z into Z?

How many homomorphisms are there of Z into Z_2?

How would you go about approaching this type of problem?

Are the following groups isomorphic?

Z_2 X Z_12 and Z_4 X Z_6

I think these are because the lcm(2,12)=lcm(4,6). Would this be a right assumption?

Z_8 X Z_10 X Z_24 and Z_4 X Z_10 X Z_40

I think these are because the lcm(8,10,24)=lcm(4,12,40)