Step 1 :
Divide $ 3526 $ by $ 478 $ and get the remainder

$$ 3526 : 478 = 7 \text{ ( remainder is } \color{blue}{ 180 } \text{ ) } $$

The remainder is positive ($ 180 > 0 $), so we will continue with division.

Step 2 :
Divide $ 478 $ by $ \color{blue}{ 180 } $ and get the remainder

$$ 478 : 180 = 2 \text{ ( remainder is } \color{blue}{ 118 } \text{ ) } $$

The remainder is still positive ($ 118 > 0 $), so we will continue with division.

Step 3 :
Divide $ 180 $ by $ \color{blue}{ 118 } $ and get the remainder

$$ 180 : 118 = 1 \text{ ( remainder is } \color{blue}{ 62 } \text{ ) } $$

The remainder is still positive ($ 62 > 0 $), so we will continue with division.

Step 4 :
Divide $ 118 $ by $ \color{blue}{ 62 } $ and get the remainder

$$ 118 : 62 = 1 \text{ ( remainder is } \color{blue}{ 56 } \text{ ) } $$

The remainder is still positive ($ 56 > 0 $), so we will continue with division.

Step 5 :
Divide $ 62 $ by $ \color{blue}{ 56 } $ and get the remainder

$$ 62 : 56 = 1 \text{ ( remainder is } \color{blue}{ 6 } \text{ ) } $$

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

Step 6 :
Divide $ 56 $ by $ \color{blue}{ 6 } $ and get the remainder

$$ 56 : 6 = 9 \text{ ( remainder is } \color{blue}{ 2 } \text{ ) } $$

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

Step 7 :
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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