Step 1 :
Divide $ 9973 $ by $ 6392 $ and get the remainder

$$ 9973 : 6392 = 1 \text{ ( remainder is } \color{blue}{ 3581 } \text{ ) } $$

The remainder is positive ($ 3581 > 0 $), so we will continue with division.

Step 2 :
Divide $ 6392 $ by $ \color{blue}{ 3581 } $ and get the remainder

$$ 6392 : 3581 = 1 \text{ ( remainder is } \color{blue}{ 2811 } \text{ ) } $$

The remainder is still positive ($ 2811 > 0 $), so we will continue with division.

Step 3 :
Divide $ 3581 $ by $ \color{blue}{ 2811 } $ and get the remainder

$$ 3581 : 2811 = 1 \text{ ( remainder is } \color{blue}{ 770 } \text{ ) } $$

The remainder is still positive ($ 770 > 0 $), so we will continue with division.

Step 4 :
Divide $ 2811 $ by $ \color{blue}{ 770 } $ and get the remainder

$$ 2811 : 770 = 3 \text{ ( remainder is } \color{blue}{ 501 } \text{ ) } $$

The remainder is still positive ($ 501 > 0 $), so we will continue with division.

Step 5 :
Divide $ 770 $ by $ \color{blue}{ 501 } $ and get the remainder

$$ 770 : 501 = 1 \text{ ( remainder is } \color{blue}{ 269 } \text{ ) } $$

The remainder is still positive ($ 269 > 0 $), so we will continue with division.

Step 6 :
Divide $ 501 $ by $ \color{blue}{ 269 } $ and get the remainder

$$ 501 : 269 = 1 \text{ ( remainder is } \color{blue}{ 232 } \text{ ) } $$

The remainder is still positive ($ 232 > 0 $), so we will continue with division.

Step 7 :
Divide $ 269 $ by $ \color{blue}{ 232 } $ and get the remainder

$$ 269 : 232 = 1 \text{ ( remainder is } \color{blue}{ 37 } \text{ ) } $$

The remainder is still positive ($ 37 > 0 $), so we will continue with division.

Step 8 :
Divide $ 232 $ by $ \color{blue}{ 37 } $ and get the remainder

$$ 232 : 37 = 6 \text{ ( remainder is } \color{blue}{ 10 } \text{ ) } $$

The remainder is still positive ($ 10 > 0 $), so we will continue with division.

Step 9 :
Divide $ 37 $ by $ \color{blue}{ 10 } $ and get the remainder

$$ 37 : 10 = 3 \text{ ( remainder is } \color{blue}{ 7 } \text{ ) } $$

The remainder is still positive ($ 7 > 0 $), so we will continue with division.

Step 10 :
Divide $ 10 $ by $ \color{blue}{ 7 } $ and get the remainder

$$ 10 : 7 = 1 \text{ ( remainder is } \color{blue}{ 3 } \text{ ) } $$

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

Step 11 :
Divide $ 7 $ by $ \color{blue}{ 3 } $ and get the remainder

$$ 7 : 3 = 2 \text{ ( remainder is } \color{blue}{ 1 } \text{ ) } $$

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

Step 12 :
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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