Finding the GCD, increasing the coefficient to 0.5 for every two passes

In the book by Rod Stevenson "Algorithms", it says:

A is the first value, B is the second, R is the remainder
It is not clear why at the end B ₁ -R ₁ = B ₁ mod R ₁

For example, for values ​​128 and 12, this is true:
A ₁ = 128, B ₁ = 12, R ₁ = 8
B ₁ -R1 = 4, B ₁ mod R ₁ = 4.
4 = 4

But, for example, for the numbers 2602 and 256 this is unfair:
A ₁ = 2602, B ₁ = 256, R ₁ = 42
B ₁ -R1 = 214, B ₁ mod R ₁ = 4
214! = 4

Or did I misunderstand something?