1. The problem is to verify the property of the greatest common divisor (GCD) for three integers $a$, $b$, and $c$: $$\text{ggT}(a,b,c) = \text{ggT}(a, \text{ggT}(b,c))$$ 2. The GCD of multiple numbers is the largest positive integer that divides all of them without leaving a remainder. 3. The property states that the GCD of three numbers can be computed by first finding the GCD of two of them, then finding the GCD of the result with the third number. 4. To understand why this holds, consider the definition: $$\text{ggT}(a,b,c) = \max\{d : d|a, d|b, d|c\}$$ and $$\text{ggT}(a, \text{ggT}(b,c)) = \max\{d : d|a, d|\text{ggT}(b,c)\}$$ 5. Since $\text{ggT}(b,c)$ divides both $b$ and $c$, any divisor of $a$ and $\text{ggT}(b,c)$ divides $a$, $b$, and $c$. 6. Therefore, both sides represent the same greatest common divisor. 7. This property allows us to compute the GCD of multiple numbers iteratively using the binary GCD operation. Final answer: $$\boxed{\text{ggT}(a,b,c) = \text{ggT}(a, \text{ggT}(b,c))}$$