Step 1 :
Divide $ 1544 $ by $ 1112 $ and get the remainder

$$ 1544 : 1112 = 1 \text{ ( remainder is } \color{blue}{ 432 } \text{ ) } $$

The remainder is positive ($ 432 > 0 $), so we will continue with division.

Step 2 :
Divide $ 1112 $ by $ \color{blue}{ 432 } $ and get the remainder

$$ 1112 : 432 = 2 \text{ ( remainder is } \color{blue}{ 248 } \text{ ) } $$

The remainder is still positive ($ 248 > 0 $), so we will continue with division.

Step 3 :
Divide $ 432 $ by $ \color{blue}{ 248 } $ and get the remainder

$$ 432 : 248 = 1 \text{ ( remainder is } \color{blue}{ 184 } \text{ ) } $$

The remainder is still positive ($ 184 > 0 $), so we will continue with division.

Step 4 :
Divide $ 248 $ by $ \color{blue}{ 184 } $ and get the remainder

$$ 248 : 184 = 1 \text{ ( remainder is } \color{blue}{ 64 } \text{ ) } $$

The remainder is still positive ($ 64 > 0 $), so we will continue with division.

Step 5 :
Divide $ 184 $ by $ \color{blue}{ 64 } $ and get the remainder

$$ 184 : 64 = 2 \text{ ( remainder is } \color{blue}{ 56 } \text{ ) } $$

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

Step 6 :
Divide $ 64 $ by $ \color{blue}{ 56 } $ and get the remainder

$$ 64 : 56 = 1 \text{ ( remainder is } \color{blue}{ 8 } \text{ ) } $$

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

Step 7 :
Divide $ 56 $ by $ \color{blue}{ 8 } $ and get the remainder

$$ 56 : \color{blue}{ \boxed { 8 }} = 7 \text{ ( remainder is } \color{blue}{ 0 } \text{ ) } $$

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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