If x and y are positive integers such that x=8y+12,what is the greatest common divisor of x and

If x and y are positive integers such that x=8y+12,what is the greatest common divisor of x and
1) x=12u,where u is an integer
2) y=12z,where z is 由题知:x=4(2y+3)
由(1)知:x=12u 则y=3k k is an integer.x=12(2k+1) 则x,y最大公因子不能确定.
由(2)知:y=12z 则x=12(6z+1) ,因此x,y的公因子是12.这个题的1 为什么最大公因子不能确定呢?2 为什么就可以呢?