Step 1 :
Divide $ 9697 $ by $ 292 $ and get the remainder

$$ 9697 : 292 = 33 \text{ ( remainder is } \color{blue}{ 61 } \text{ ) } $$

The remainder is positive ($ 61 > 0 $), so we will continue with division.

Step 2 :
Divide $ 292 $ by $ \color{blue}{ 61 } $ and get the remainder

$$ 292 : 61 = 4 \text{ ( remainder is } \color{blue}{ 48 } \text{ ) } $$

The remainder is still positive ($ 48 > 0 $), so we will continue with division.

Step 3 :
Divide $ 61 $ by $ \color{blue}{ 48 } $ and get the remainder

$$ 61 : 48 = 1 \text{ ( remainder is } \color{blue}{ 13 } \text{ ) } $$

The remainder is still positive ($ 13 > 0 $), so we will continue with division.

Step 4 :
Divide $ 48 $ by $ \color{blue}{ 13 } $ and get the remainder

$$ 48 : 13 = 3 \text{ ( remainder is } \color{blue}{ 9 } \text{ ) } $$

The remainder is still positive ($ 9 > 0 $), so we will continue with division.

Step 5 :
Divide $ 13 $ by $ \color{blue}{ 9 } $ and get the remainder

$$ 13 : 9 = 1 \text{ ( remainder is } \color{blue}{ 4 } \text{ ) } $$

The remainder is still positive ($ 4 > 0 $), so we will continue with division.

Step 6 :
Divide $ 9 $ by $ \color{blue}{ 4 } $ and get the remainder

$$ 9 : 4 = 2 \text{ ( remainder is } \color{blue}{ 1 } \text{ ) } $$

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

Step 7 :
Divide $ 4 $ by $ \color{blue}{ 1 } $ and get the remainder

$$ 4 : \color{blue}{ \boxed { 1 }} = 4 \text{ ( remainder is } \color{blue}{ 0 } \text{ ) } $$

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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