Step 1 :
Divide $ 912 $ by $ 345 $ and get the remainder

$$ 912 : 345 = 2 \text{ ( remainder is } \color{blue}{ 222 } \text{ ) } $$

The remainder is positive ($ 222 > 0 $), so we will continue with division.

Step 2 :
Divide $ 345 $ by $ \color{blue}{ 222 } $ and get the remainder

$$ 345 : 222 = 1 \text{ ( remainder is } \color{blue}{ 123 } \text{ ) } $$

The remainder is still positive ($ 123 > 0 $), so we will continue with division.

Step 3 :
Divide $ 222 $ by $ \color{blue}{ 123 } $ and get the remainder

$$ 222 : 123 = 1 \text{ ( remainder is } \color{blue}{ 99 } \text{ ) } $$

The remainder is still positive ($ 99 > 0 $), so we will continue with division.

Step 4 :
Divide $ 123 $ by $ \color{blue}{ 99 } $ and get the remainder

$$ 123 : 99 = 1 \text{ ( remainder is } \color{blue}{ 24 } \text{ ) } $$

The remainder is still positive ($ 24 > 0 $), so we will continue with division.

Step 5 :
Divide $ 99 $ by $ \color{blue}{ 24 } $ and get the remainder

$$ 99 : 24 = 4 \text{ ( remainder is } \color{blue}{ 3 } \text{ ) } $$

The remainder is still positive ($ 3 > 0 $), so we will continue with division.

Step 6 :
Divide $ 24 $ by $ \color{blue}{ 3 } $ and get the remainder

$$ 24 : \color{blue}{ \boxed { 3 }} = 8 \text{ ( remainder is } \color{blue}{ 0 } \text{ ) } $$

The remainder is zero => GCD is the last divisor $ \color{blue}{ \boxed { 3 }} $.

This solution can be visualized using a Venn diagram.

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

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