Step 1 :
Divide $ 7234 $ by $ 3476 $ and get the remainder

$$ 7234 : 3476 = 2 \text{ ( remainder is } \color{blue}{ 282 } \text{ ) } $$

The remainder is positive ($ 282 > 0 $), so we will continue with division.

Step 2 :
Divide $ 3476 $ by $ \color{blue}{ 282 } $ and get the remainder

$$ 3476 : 282 = 12 \text{ ( remainder is } \color{blue}{ 92 } \text{ ) } $$

The remainder is still positive ($ 92 > 0 $), so we will continue with division.

Step 3 :
Divide $ 282 $ by $ \color{blue}{ 92 } $ and get the remainder

$$ 282 : 92 = 3 \text{ ( remainder is } \color{blue}{ 6 } \text{ ) } $$

The remainder is still positive ($ 6 > 0 $), so we will continue with division.

Step 4 :
Divide $ 92 $ by $ \color{blue}{ 6 } $ and get the remainder

$$ 92 : 6 = 15 \text{ ( remainder is } \color{blue}{ 2 } \text{ ) } $$

The remainder is still positive ($ 2 > 0 $), so we will continue with division.

Step 5 :
Divide $ 6 $ by $ \color{blue}{ 2 } $ and get the remainder

$$ 6 : \color{blue}{ \boxed { 2 }} = 3 \text{ ( remainder is } \color{blue}{ 0 } \text{ ) } $$

The remainder is zero => GCD is the last divisor $ \color{blue}{ \boxed { 2 }} $.

This solution can be visualized using a Venn diagram.

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

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