Step 1 :
Divide $ 215 $ by $ 81 $ and get the remainder

$$ 215 : 81 = 2 \text{ ( remainder is } \color{blue}{ 53 } \text{ ) } $$

The remainder is positive ($ 53 > 0 $), so we will continue with division.

Step 2 :
Divide $ 81 $ by $ \color{blue}{ 53 } $ and get the remainder

$$ 81 : 53 = 1 \text{ ( remainder is } \color{blue}{ 28 } \text{ ) } $$

The remainder is still positive ($ 28 > 0 $), so we will continue with division.

Step 3 :
Divide $ 53 $ by $ \color{blue}{ 28 } $ and get the remainder

$$ 53 : 28 = 1 \text{ ( remainder is } \color{blue}{ 25 } \text{ ) } $$

The remainder is still positive ($ 25 > 0 $), so we will continue with division.

Step 4 :
Divide $ 28 $ by $ \color{blue}{ 25 } $ and get the remainder

$$ 28 : 25 = 1 \text{ ( remainder is } \color{blue}{ 3 } \text{ ) } $$

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

Step 5 :
Divide $ 25 $ by $ \color{blue}{ 3 } $ and get the remainder

$$ 25 : 3 = 8 \text{ ( remainder is } \color{blue}{ 1 } \text{ ) } $$

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

Step 6 :
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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