The sum of two numbers is 136. one number is 51. what is the other number? what are the common factors of these two numbers?

 You said that                            51 + (the other number) = 136 .

This is an equation.
I can do anything I want to one side of it,
as long as I do exactly the same thing to
the other side.

Let's subtract  51  from each side:  (the other number) =  136 - 51

                                                                                     =  85 .

The factors of 51 are  1,  3,  17,  and 51 .

The factors of  85  are  1,  5,  17, and 85 .

The common factors are  1  and  17 .