A COMMON FACTOR MEANS A NUMBER - THAT EXISTS BETWEEN TWO NUMBERS 8 , AND 12 THAT CAN BE USED TO PRODUCE EITHER . 8 = 1X 2 X4,    12 = 1X 2 X  2  x 3 .   IF YOU SEE  BY COMPARING  THE , 8 and the 12  THEN NOW ,  one 1   in the 8 . AND YOhtU SEE  one  1, in the 12 there?   So would those  factors be  the greatest common factor?  If not , then which one would be? 

There's the greatest common factor ; did you say 2 ?  Look again  a little more ;  at  the 12 =   what?

1   x   2   x  2  x  3   ,  Right? So 1  isn't it.  And   2  or   3   isn't it. But  we are allowed to  use  the 2  x  2  . What do we get?  Did you say   4?    Right! The greatest common factor is 4.