If z is an integer, is Z/4 also an integer?

1) z is a factor of 24.
2) Z/3 is an integer.


I opted for A but its a wrong answer.... but why...?

From 1: If z is a factor of 24 meaning Z must be divisible by 4 and therefore Z/4 has to be an integer. Sufficient

From 2: Lets take z as 12 then Z/3 is an integer and Z/4 also is an integer But if we take Z as 9 then Z/3 is an integer but Z/4 is not an integer. Not Sufficient

Where am i going wrong