jmc

We can perform the Euclidean Algorithm two times.

First, we use it for $3339$ and $2961$. $$\begin{array}{rl}\text{gcd}(3339,2961)& =\text{gcd}(3339-2961,2961)\\ & =\text{gcd}(378,2961)\\ & =\text{gcd}(378,2961-378\cdot 7)\\ & =\text{gcd}(378,315)\\ & =\text{gcd}(378-315,315)\\ & =\text{gcd}(63,315)\end{array}$$Since $63$ is a divisor of $315$, the greatest common divisor of $3339$ and $2961$ is $63$.

Next, we can find the greatest common divisor of $63$ and $1491$, also using the Euclidean Algorithm. $$\begin{array}{rl}\text{gcd}(63,1491)& =\text{gcd}(63,1491-63\cdot 23)\\ & =\text{gcd}(63,42)\end{array}$$Since $63=3\cdot 21$ and $42=2\cdot 21$, the greatest common divisor is $\boxed{21}$.