Step 1 :
Divide $ 3564 $ by $ 926 $ and get the remainder

$$ 3564 : 926 = 3 \text{ ( remainder is } \color{blue}{ 786 } \text{ ) } $$

The remainder is positive ($ 786 > 0 $), so we will continue with division.

Step 2 :
Divide $ 926 $ by $ \color{blue}{ 786 } $ and get the remainder

$$ 926 : 786 = 1 \text{ ( remainder is } \color{blue}{ 140 } \text{ ) } $$

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

Step 3 :
Divide $ 786 $ by $ \color{blue}{ 140 } $ and get the remainder

$$ 786 : 140 = 5 \text{ ( remainder is } \color{blue}{ 86 } \text{ ) } $$

The remainder is still positive ($ 86 > 0 $), so we will continue with division.

Step 4 :
Divide $ 140 $ by $ \color{blue}{ 86 } $ and get the remainder

$$ 140 : 86 = 1 \text{ ( remainder is } \color{blue}{ 54 } \text{ ) } $$

The remainder is still positive ($ 54 > 0 $), so we will continue with division.

Step 5 :
Divide $ 86 $ by $ \color{blue}{ 54 } $ and get the remainder

$$ 86 : 54 = 1 \text{ ( remainder is } \color{blue}{ 32 } \text{ ) } $$

The remainder is still positive ($ 32 > 0 $), so we will continue with division.

Step 6 :
Divide $ 54 $ by $ \color{blue}{ 32 } $ and get the remainder

$$ 54 : 32 = 1 \text{ ( remainder is } \color{blue}{ 22 } \text{ ) } $$

The remainder is still positive ($ 22 > 0 $), so we will continue with division.

Step 7 :
Divide $ 32 $ by $ \color{blue}{ 22 } $ and get the remainder

$$ 32 : 22 = 1 \text{ ( remainder is } \color{blue}{ 10 } \text{ ) } $$

The remainder is still positive ($ 10 > 0 $), so we will continue with division.

Step 8 :
Divide $ 22 $ by $ \color{blue}{ 10 } $ and get the remainder

$$ 22 : 10 = 2 \text{ ( remainder is } \color{blue}{ 2 } \text{ ) } $$

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

Step 9 :
Divide $ 10 $ by $ \color{blue}{ 2 } $ and get the remainder

$$ 10 : \color{blue}{ \boxed { 2 }} = 5 \text{ ( remainder is } \color{blue}{ 0 } \text{ ) } $$

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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