Step 1 :
Divide $ 6751 $ by $ 5436 $ and get the remainder

$$ 6751 : 5436 = 1 \text{ ( remainder is } \color{blue}{ 1315 } \text{ ) } $$

The remainder is positive ($ 1315 > 0 $), so we will continue with division.

Step 2 :
Divide $ 5436 $ by $ \color{blue}{ 1315 } $ and get the remainder

$$ 5436 : 1315 = 4 \text{ ( remainder is } \color{blue}{ 176 } \text{ ) } $$

The remainder is still positive ($ 176 > 0 $), so we will continue with division.

Step 3 :
Divide $ 1315 $ by $ \color{blue}{ 176 } $ and get the remainder

$$ 1315 : 176 = 7 \text{ ( remainder is } \color{blue}{ 83 } \text{ ) } $$

The remainder is still positive ($ 83 > 0 $), so we will continue with division.

Step 4 :
Divide $ 176 $ by $ \color{blue}{ 83 } $ and get the remainder

$$ 176 : 83 = 2 \text{ ( remainder is } \color{blue}{ 10 } \text{ ) } $$

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

Step 5 :
Divide $ 83 $ by $ \color{blue}{ 10 } $ and get the remainder

$$ 83 : 10 = 8 \text{ ( remainder is } \color{blue}{ 3 } \text{ ) } $$

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

Step 6 :
Divide $ 10 $ by $ \color{blue}{ 3 } $ and get the remainder

$$ 10 : 3 = 3 \text{ ( remainder is } \color{blue}{ 1 } \text{ ) } $$

The remainder is still positive ($ 1 > 0 $), so we will continue with division.

Step 7 :
Divide $ 3 $ by $ \color{blue}{ 1 } $ and get the remainder

$$ 3 : \color{blue}{ \boxed { 1 }} = 3 \text{ ( remainder is } \color{blue}{ 0 } \text{ ) } $$

The remainder is zero => GCD is the last divisor $ \color{blue}{ \boxed { 1 }} $.

This solution can be visualized using a Venn diagram.

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

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