Step 1 :
Divide $ 1078 $ by $ 672 $ and get the remainder

$$ 1078 : 672 = 1 \text{ ( remainder is } \color{blue}{ 406 } \text{ ) } $$

The remainder is positive ($ 406 > 0 $), so we will continue with division.

Step 2 :
Divide $ 672 $ by $ \color{blue}{ 406 } $ and get the remainder

$$ 672 : 406 = 1 \text{ ( remainder is } \color{blue}{ 266 } \text{ ) } $$

The remainder is still positive ($ 266 > 0 $), so we will continue with division.

Step 3 :
Divide $ 406 $ by $ \color{blue}{ 266 } $ and get the remainder

$$ 406 : 266 = 1 \text{ ( remainder is } \color{blue}{ 140 } \text{ ) } $$

The remainder is still positive ($ 140 > 0 $), so we will continue with division.

Step 4 :
Divide $ 266 $ by $ \color{blue}{ 140 } $ and get the remainder

$$ 266 : 140 = 1 \text{ ( remainder is } \color{blue}{ 126 } \text{ ) } $$

The remainder is still positive ($ 126 > 0 $), so we will continue with division.

Step 5 :
Divide $ 140 $ by $ \color{blue}{ 126 } $ and get the remainder

$$ 140 : 126 = 1 \text{ ( remainder is } \color{blue}{ 14 } \text{ ) } $$

The remainder is still positive ($ 14 > 0 $), so we will continue with division.

Step 6 :
Divide $ 126 $ by $ \color{blue}{ 14 } $ and get the remainder

$$ 126 : \color{blue}{ \boxed { 14 }} = 9 \text{ ( remainder is } \color{blue}{ 0 } \text{ ) } $$

The remainder is zero => GCD is the last divisor $ \color{blue}{ \boxed { 14 }} $.

This solution can be visualized using a Venn diagram.

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

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