How you can find the common factors and the greatest common factor of two numbers

One way is to create a factor tree for each number.  Then see which factors they have in common.

Example:

   12                30

   ^                  ^

2    6             3  10

      ^                   ^

    2  3               2  5

The factors are the underlined numbers above:

12: 2 x 2 x 3

30: 2 x 3 x 5

The common factors are: 2, 3, and 6    why 6? because 2 x 3 = 6

The greatest common factor is: 6

for the friend request.

when a figure, such as triangle (xyz) is reflected over the line y = x to create x'y'z' the x-coordinates and y-coordinates of the original image (pre-image) will be reversed for the image. (e.g., (x, y) > (y, x)) this means that the pre-image position of the x- and y-coordinates switch places which in turn provides a mirror like image of the original xyz.  

i notice that when i draw a line segment from x to x', that the points are parallel from each other -- they are exactly across from each other and do not intersect with any other points.  

yes, think i would see the same characteristic if you drew the line segment connecting y with the reflecting line and then y' with the reflecting line because of the essence of reflections. because it is a mirror image, each point was effected the same way which leads me to conclude that they same would apply to y and y'.