Step 1 :
Divide $ 442 $ by $ 272 $ and get the remainder

$$ 442 : 272 = 1 \text{ ( remainder is } \color{blue}{ 170 } \text{ ) } $$

The remainder is positive ($ 170 > 0 $), so we will continue with division.

Step 2 :
Divide $ 272 $ by $ \color{blue}{ 170 } $ and get the remainder

$$ 272 : 170 = 1 \text{ ( remainder is } \color{blue}{ 102 } \text{ ) } $$

The remainder is still positive ($ 102 > 0 $), so we will continue with division.

Step 3 :
Divide $ 170 $ by $ \color{blue}{ 102 } $ and get the remainder

$$ 170 : 102 = 1 \text{ ( remainder is } \color{blue}{ 68 } \text{ ) } $$

The remainder is still positive ($ 68 > 0 $), so we will continue with division.

Step 4 :
Divide $ 102 $ by $ \color{blue}{ 68 } $ and get the remainder

$$ 102 : 68 = 1 \text{ ( remainder is } \color{blue}{ 34 } \text{ ) } $$

The remainder is still positive ($ 34 > 0 $), so we will continue with division.

Step 5 :
Divide $ 68 $ by $ \color{blue}{ 34 } $ and get the remainder

$$ 68 : \color{blue}{ \boxed { 34 }} = 2 \text{ ( remainder is } \color{blue}{ 0 } \text{ ) } $$

The remainder is zero => GCD is the last divisor $ \color{blue}{ \boxed { 34 }} $.

This solution can be visualized using a Venn diagram.

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

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