Step 1 :
Divide $ 15712 $ by $ 12344 $ and get the remainder

$$ 15712 : 12344 = 1 \text{ ( remainder is } \color{blue}{ 3368 } \text{ ) } $$

The remainder is positive ($ 3368 > 0 $), so we will continue with division.

Step 2 :
Divide $ 12344 $ by $ \color{blue}{ 3368 } $ and get the remainder

$$ 12344 : 3368 = 3 \text{ ( remainder is } \color{blue}{ 2240 } \text{ ) } $$

The remainder is still positive ($ 2240 > 0 $), so we will continue with division.

Step 3 :
Divide $ 3368 $ by $ \color{blue}{ 2240 } $ and get the remainder

$$ 3368 : 2240 = 1 \text{ ( remainder is } \color{blue}{ 1128 } \text{ ) } $$

The remainder is still positive ($ 1128 > 0 $), so we will continue with division.

Step 4 :
Divide $ 2240 $ by $ \color{blue}{ 1128 } $ and get the remainder

$$ 2240 : 1128 = 1 \text{ ( remainder is } \color{blue}{ 1112 } \text{ ) } $$

The remainder is still positive ($ 1112 > 0 $), so we will continue with division.

Step 5 :
Divide $ 1128 $ by $ \color{blue}{ 1112 } $ and get the remainder

$$ 1128 : 1112 = 1 \text{ ( remainder is } \color{blue}{ 16 } \text{ ) } $$

The remainder is still positive ($ 16 > 0 $), so we will continue with division.

Step 6 :
Divide $ 1112 $ by $ \color{blue}{ 16 } $ and get the remainder

$$ 1112 : 16 = 69 \text{ ( remainder is } \color{blue}{ 8 } \text{ ) } $$

The remainder is still positive ($ 8 > 0 $), so we will continue with division.

Step 7 :
Divide $ 16 $ by $ \color{blue}{ 8 } $ and get the remainder

$$ 16 : \color{blue}{ \boxed { 8 }} = 2 \text{ ( remainder is } \color{blue}{ 0 } \text{ ) } $$

The remainder is zero => GCD is the last divisor $ \color{blue}{ \boxed { 8 }} $.

This solution can be visualized using a Venn diagram.

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

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