Finding a greatest common divisor

Solution 1: We can use the Euclidean Algorithm .

$\begin{array}{rcl} \gcd(2982,2016) & = & \gcd(2016, 966)\\ & = & \gcd(966, 84)\\ & = & \gcd(84,42)\\ & = & \gcd(42,0)\\ & = & 42.\\ \end{array}$

Solution 2: We can factor $2982 = 2 \times 3 \times 7 \times 71$ and $2016 = 2^5 \times 3^2 \times 7$ . Then

$\gcd(2982,2016) = 2^{1} \times 3^{1} \times 7^{1} = 42.$