Step 1 :
Divide $ 3125 $ by $ 21 $ and get the remainder

$$ 3125 : 21 = 148 \text{ ( remainder is } \color{blue}{ 17 } \text{ ) } $$

The remainder is positive ($ 17 > 0 $), so we will continue with division.

Step 2 :
Divide $ 21 $ by $ \color{blue}{ 17 } $ and get the remainder

$$ 21 : 17 = 1 \text{ ( remainder is } \color{blue}{ 4 } \text{ ) } $$

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

Step 3 :
Divide $ 17 $ by $ \color{blue}{ 4 } $ and get the remainder

$$ 17 : 4 = 4 \text{ ( remainder is } \color{blue}{ 1 } \text{ ) } $$

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

Step 4 :
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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