Step 1 :
Divide $ 1625 $ by $ 975 $ and get the remainder

$$ 1625 : 975 = 1 \text{ ( remainder is } \color{blue}{ 650 } \text{ ) } $$

The remainder is positive ($ 650 > 0 $), so we will continue with division.

Step 2 :
Divide $ 975 $ by $ \color{blue}{ 650 } $ and get the remainder

$$ 975 : 650 = 1 \text{ ( remainder is } \color{blue}{ 325 } \text{ ) } $$

The remainder is still positive ($ 325 > 0 $), so we will continue with division.

Step 3 :
Divide $ 650 $ by $ \color{blue}{ 325 } $ and get the remainder

$$ 650 : \color{blue}{ \boxed { 325 }} = 2 \text{ ( remainder is } \color{blue}{ 0 } \text{ ) } $$

The remainder is zero => GCD is the last divisor $ \color{blue}{ \boxed { 325 }} $.

This solution can be visualized using a Venn diagram.

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

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