Step 1 :
Divide $ 9357 $ by $ 5864 $ and get the remainder

$$ 9357 : 5864 = 1 \text{ ( remainder is } \color{blue}{ 3493 } \text{ ) } $$

The remainder is positive ($ 3493 > 0 $), so we will continue with division.

Step 2 :
Divide $ 5864 $ by $ \color{blue}{ 3493 } $ and get the remainder

$$ 5864 : 3493 = 1 \text{ ( remainder is } \color{blue}{ 2371 } \text{ ) } $$

The remainder is still positive ($ 2371 > 0 $), so we will continue with division.

Step 3 :
Divide $ 3493 $ by $ \color{blue}{ 2371 } $ and get the remainder

$$ 3493 : 2371 = 1 \text{ ( remainder is } \color{blue}{ 1122 } \text{ ) } $$

The remainder is still positive ($ 1122 > 0 $), so we will continue with division.

Step 4 :
Divide $ 2371 $ by $ \color{blue}{ 1122 } $ and get the remainder

$$ 2371 : 1122 = 2 \text{ ( remainder is } \color{blue}{ 127 } \text{ ) } $$

The remainder is still positive ($ 127 > 0 $), so we will continue with division.

Step 5 :
Divide $ 1122 $ by $ \color{blue}{ 127 } $ and get the remainder

$$ 1122 : 127 = 8 \text{ ( remainder is } \color{blue}{ 106 } \text{ ) } $$

The remainder is still positive ($ 106 > 0 $), so we will continue with division.

Step 6 :
Divide $ 127 $ by $ \color{blue}{ 106 } $ and get the remainder

$$ 127 : 106 = 1 \text{ ( remainder is } \color{blue}{ 21 } \text{ ) } $$

The remainder is still positive ($ 21 > 0 $), so we will continue with division.

Step 7 :
Divide $ 106 $ by $ \color{blue}{ 21 } $ and get the remainder

$$ 106 : 21 = 5 \text{ ( remainder is } \color{blue}{ 1 } \text{ ) } $$

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

Step 8 :
Divide $ 21 $ by $ \color{blue}{ 1 } $ and get the remainder

$$ 21 : \color{blue}{ \boxed { 1 }} = 21 \text{ ( remainder is } \color{blue}{ 0 } \text{ ) } $$

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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