Step 1 :
Divide $ 2016 $ by $ 927 $ and get the remainder

$$ 2016 : 927 = 2 \text{ ( remainder is } \color{blue}{ 162 } \text{ ) } $$

The remainder is positive ($ 162 > 0 $), so we will continue with division.

Step 2 :
Divide $ 927 $ by $ \color{blue}{ 162 } $ and get the remainder

$$ 927 : 162 = 5 \text{ ( remainder is } \color{blue}{ 117 } \text{ ) } $$

The remainder is still positive ($ 117 > 0 $), so we will continue with division.

Step 3 :
Divide $ 162 $ by $ \color{blue}{ 117 } $ and get the remainder

$$ 162 : 117 = 1 \text{ ( remainder is } \color{blue}{ 45 } \text{ ) } $$

The remainder is still positive ($ 45 > 0 $), so we will continue with division.

Step 4 :
Divide $ 117 $ by $ \color{blue}{ 45 } $ and get the remainder

$$ 117 : 45 = 2 \text{ ( remainder is } \color{blue}{ 27 } \text{ ) } $$

The remainder is still positive ($ 27 > 0 $), so we will continue with division.

Step 5 :
Divide $ 45 $ by $ \color{blue}{ 27 } $ and get the remainder

$$ 45 : 27 = 1 \text{ ( remainder is } \color{blue}{ 18 } \text{ ) } $$

The remainder is still positive ($ 18 > 0 $), so we will continue with division.

Step 6 :
Divide $ 27 $ by $ \color{blue}{ 18 } $ and get the remainder

$$ 27 : 18 = 1 \text{ ( remainder is } \color{blue}{ 9 } \text{ ) } $$

The remainder is still positive ($ 9 > 0 $), so we will continue with division.

Step 7 :
Divide $ 18 $ by $ \color{blue}{ 9 } $ and get the remainder

$$ 18 : \color{blue}{ \boxed { 9 }} = 2 \text{ ( remainder is } \color{blue}{ 0 } \text{ ) } $$

The remainder is zero => GCD is the last divisor $ \color{blue}{ \boxed { 9 }} $.

This solution can be visualized using a Venn diagram.

The GCD equals the product of the numbers at the intersection.

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