I did not understand your first question as it is not clear what is x,y, m or n? Please rephrase it clearly.

For second question let us say n = 2, so consecutive multiples of 2 are 2,4,6,8,10.....

The Greatest Common factor of 2(2*1),4(2*2),6(2*3),8(2*24),10(2*5)..... is 2, which is equal to n.

Hope this makes sense!!!

I believe your first question is:- why the GCF of x and y can't be > x - y?

This is only possible if x and y are distinct; x and y are not consecutive multiples of a certain number.

e.g. x = y = 10. GCF = 10 is > 10 - 10 (0)

e.g. x = 2, y = 4. GCF = 2 is = 4 - 2 (2)

For all cases GCF can't be greater than the difference.

e.g. x = 12, y = 28. GCF = 4 is < 28 - 12 (16)

e.g. x = 5, y = 3. GCF = 1 is < 5 - 3 (2)

Note:- Maximum value of GCF of x and y can be smaller of the two values(cases such as x =4, y = 8 and GCF is 4 here) in all other cases GCF will always be 1 <= GCF <= smaller of the two values.