jmc

We can use the Euclidean Algorithm to find the greatest common divisor of these two integers. $$\begin{array}{rl}\gcd (7979,3713)& =\gcd (3713,7979-2\cdot 3713)\\ & =\gcd (3713,553)\\ & =\gcd (553,3713-6\cdot 553)\\ & =\gcd (553,395)\\ & =\gcd (395,553-395)\\ & =\gcd (395,158)\\ & =\gcd (158,395-2\cdot 158)\\ & =\gcd (158,79)\\ & =\boxed{79}.\end{array}$$