Step 1 :
Divide $ 13527 $ by $ 4237 $ and get the remainder

$$ 13527 : 4237 = 3 \text{ ( remainder is } \color{blue}{ 816 } \text{ ) } $$

The remainder is positive ($ 816 > 0 $), so we will continue with division.

Step 2 :
Divide $ 4237 $ by $ \color{blue}{ 816 } $ and get the remainder

$$ 4237 : 816 = 5 \text{ ( remainder is } \color{blue}{ 157 } \text{ ) } $$

The remainder is still positive ($ 157 > 0 $), so we will continue with division.

Step 3 :
Divide $ 816 $ by $ \color{blue}{ 157 } $ and get the remainder

$$ 816 : 157 = 5 \text{ ( remainder is } \color{blue}{ 31 } \text{ ) } $$

The remainder is still positive ($ 31 > 0 $), so we will continue with division.

Step 4 :
Divide $ 157 $ by $ \color{blue}{ 31 } $ and get the remainder

$$ 157 : 31 = 5 \text{ ( remainder is } \color{blue}{ 2 } \text{ ) } $$

The remainder is still positive ($ 2 > 0 $), so we will continue with division.

Step 5 :
Divide $ 31 $ by $ \color{blue}{ 2 } $ and get the remainder

$$ 31 : 2 = 15 \text{ ( remainder is } \color{blue}{ 1 } \text{ ) } $$

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

Step 6 :
Divide $ 2 $ by $ \color{blue}{ 1 } $ and get the remainder

$$ 2 : \color{blue}{ \boxed { 1 }} = 2 \text{ ( remainder is } \color{blue}{ 0 } \text{ ) } $$

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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