Step 1 :
Divide $ 9973 $ by $ 6393 $ and get the remainder

$$ 9973 : 6393 = 1 \text{ ( remainder is } \color{blue}{ 3580 } \text{ ) } $$

The remainder is positive ($ 3580 > 0 $), so we will continue with division.

Step 2 :
Divide $ 6393 $ by $ \color{blue}{ 3580 } $ and get the remainder

$$ 6393 : 3580 = 1 \text{ ( remainder is } \color{blue}{ 2813 } \text{ ) } $$

The remainder is still positive ($ 2813 > 0 $), so we will continue with division.

Step 3 :
Divide $ 3580 $ by $ \color{blue}{ 2813 } $ and get the remainder

$$ 3580 : 2813 = 1 \text{ ( remainder is } \color{blue}{ 767 } \text{ ) } $$

The remainder is still positive ($ 767 > 0 $), so we will continue with division.

Step 4 :
Divide $ 2813 $ by $ \color{blue}{ 767 } $ and get the remainder

$$ 2813 : 767 = 3 \text{ ( remainder is } \color{blue}{ 512 } \text{ ) } $$

The remainder is still positive ($ 512 > 0 $), so we will continue with division.

Step 5 :
Divide $ 767 $ by $ \color{blue}{ 512 } $ and get the remainder

$$ 767 : 512 = 1 \text{ ( remainder is } \color{blue}{ 255 } \text{ ) } $$

The remainder is still positive ($ 255 > 0 $), so we will continue with division.

Step 6 :
Divide $ 512 $ by $ \color{blue}{ 255 } $ and get the remainder

$$ 512 : 255 = 2 \text{ ( remainder is } \color{blue}{ 2 } \text{ ) } $$

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

Step 7 :
Divide $ 255 $ by $ \color{blue}{ 2 } $ and get the remainder

$$ 255 : 2 = 127 \text{ ( remainder is } \color{blue}{ 1 } \text{ ) } $$

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

Step 8 :
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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