Step 1 :
Divide $ 57608 $ by $ 14580 $ and get the remainder

$$ 57608 : 14580 = 3 \text{ ( remainder is } \color{blue}{ 13868 } \text{ ) } $$

The remainder is positive ($ 13868 > 0 $), so we will continue with division.

Step 2 :
Divide $ 14580 $ by $ \color{blue}{ 13868 } $ and get the remainder

$$ 14580 : 13868 = 1 \text{ ( remainder is } \color{blue}{ 712 } \text{ ) } $$

The remainder is still positive ($ 712 > 0 $), so we will continue with division.

Step 3 :
Divide $ 13868 $ by $ \color{blue}{ 712 } $ and get the remainder

$$ 13868 : 712 = 19 \text{ ( remainder is } \color{blue}{ 340 } \text{ ) } $$

The remainder is still positive ($ 340 > 0 $), so we will continue with division.

Step 4 :
Divide $ 712 $ by $ \color{blue}{ 340 } $ and get the remainder

$$ 712 : 340 = 2 \text{ ( remainder is } \color{blue}{ 32 } \text{ ) } $$

The remainder is still positive ($ 32 > 0 $), so we will continue with division.

Step 5 :
Divide $ 340 $ by $ \color{blue}{ 32 } $ and get the remainder

$$ 340 : 32 = 10 \text{ ( remainder is } \color{blue}{ 20 } \text{ ) } $$

The remainder is still positive ($ 20 > 0 $), so we will continue with division.

Step 6 :
Divide $ 32 $ by $ \color{blue}{ 20 } $ and get the remainder

$$ 32 : 20 = 1 \text{ ( remainder is } \color{blue}{ 12 } \text{ ) } $$

The remainder is still positive ($ 12 > 0 $), so we will continue with division.

Step 7 :
Divide $ 20 $ by $ \color{blue}{ 12 } $ and get the remainder

$$ 20 : 12 = 1 \text{ ( remainder is } \color{blue}{ 8 } \text{ ) } $$

The remainder is still positive ($ 8 > 0 $), so we will continue with division.

Step 8 :
Divide $ 12 $ by $ \color{blue}{ 8 } $ and get the remainder

$$ 12 : 8 = 1 \text{ ( remainder is } \color{blue}{ 4 } \text{ ) } $$

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

Step 9 :
Divide $ 8 $ by $ \color{blue}{ 4 } $ and get the remainder

$$ 8 : \color{blue}{ \boxed { 4 }} = 2 \text{ ( remainder is } \color{blue}{ 0 } \text{ ) } $$

The remainder is zero => GCD is the last divisor $ \color{blue}{ \boxed { 4 }} $.

This solution can be visualized using a Venn diagram.

The GCD equals the product of the numbers at the intersection.

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