Step 1 :
Divide $ 756 $ by $ 537 $ and get the remainder

$$ 756 : 537 = 1 \text{ ( remainder is } \color{blue}{ 219 } \text{ ) } $$

The remainder is positive ($ 219 > 0 $), so we will continue with division.

Step 2 :
Divide $ 537 $ by $ \color{blue}{ 219 } $ and get the remainder

$$ 537 : 219 = 2 \text{ ( remainder is } \color{blue}{ 99 } \text{ ) } $$

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

Step 3 :
Divide $ 219 $ by $ \color{blue}{ 99 } $ and get the remainder

$$ 219 : 99 = 2 \text{ ( remainder is } \color{blue}{ 21 } \text{ ) } $$

The remainder is still positive ($ 21 > 0 $), so we will continue with division.

Step 4 :
Divide $ 99 $ by $ \color{blue}{ 21 } $ and get the remainder

$$ 99 : 21 = 4 \text{ ( remainder is } \color{blue}{ 15 } \text{ ) } $$

The remainder is still positive ($ 15 > 0 $), so we will continue with division.

Step 5 :
Divide $ 21 $ by $ \color{blue}{ 15 } $ and get the remainder

$$ 21 : 15 = 1 \text{ ( remainder is } \color{blue}{ 6 } \text{ ) } $$

The remainder is still positive ($ 6 > 0 $), so we will continue with division.

Step 6 :
Divide $ 15 $ by $ \color{blue}{ 6 } $ and get the remainder

$$ 15 : 6 = 2 \text{ ( remainder is } \color{blue}{ 3 } \text{ ) } $$

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

Step 7 :
Divide $ 6 $ by $ \color{blue}{ 3 } $ and get the remainder

$$ 6 : \color{blue}{ \boxed { 3 }} = 2 \text{ ( remainder is } \color{blue}{ 0 } \text{ ) } $$

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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