Step 1 :
Divide $ 340 $ by $ 220 $ and get the remainder

$$ 340 : 220 = 1 \text{ ( remainder is } \color{blue}{ 120 } \text{ ) } $$

The remainder is positive ($ 120 > 0 $), so we will continue with division.

Step 2 :
Divide $ 220 $ by $ \color{blue}{ 120 } $ and get the remainder

$$ 220 : 120 = 1 \text{ ( remainder is } \color{blue}{ 100 } \text{ ) } $$

The remainder is still positive ($ 100 > 0 $), so we will continue with division.

Step 3 :
Divide $ 120 $ by $ \color{blue}{ 100 } $ and get the remainder

$$ 120 : 100 = 1 \text{ ( remainder is } \color{blue}{ 20 } \text{ ) } $$

The remainder is still positive ($ 20 > 0 $), so we will continue with division.

Step 4 :
Divide $ 100 $ by $ \color{blue}{ 20 } $ and get the remainder

$$ 100 : \color{blue}{ \boxed { 20 }} = 5 \text{ ( remainder is } \color{blue}{ 0 } \text{ ) } $$

The remainder is zero => GCD is the last divisor $ \color{blue}{ \boxed { 20 }} $.

This solution can be visualized using a Venn diagram.

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

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