Step 1 :
Divide $ 3915 $ by $ 825 $ and get the remainder

$$ 3915 : 825 = 4 \text{ ( remainder is } \color{blue}{ 615 } \text{ ) } $$

The remainder is positive ($ 615 > 0 $), so we will continue with division.

Step 2 :
Divide $ 825 $ by $ \color{blue}{ 615 } $ and get the remainder

$$ 825 : 615 = 1 \text{ ( remainder is } \color{blue}{ 210 } \text{ ) } $$

The remainder is still positive ($ 210 > 0 $), so we will continue with division.

Step 3 :
Divide $ 615 $ by $ \color{blue}{ 210 } $ and get the remainder

$$ 615 : 210 = 2 \text{ ( remainder is } \color{blue}{ 195 } \text{ ) } $$

The remainder is still positive ($ 195 > 0 $), so we will continue with division.

Step 4 :
Divide $ 210 $ by $ \color{blue}{ 195 } $ and get the remainder

$$ 210 : 195 = 1 \text{ ( remainder is } \color{blue}{ 15 } \text{ ) } $$

The remainder is still positive ($ 15 > 0 $), so we will continue with division.

Step 5 :
Divide $ 195 $ by $ \color{blue}{ 15 } $ and get the remainder

$$ 195 : \color{blue}{ \boxed { 15 }} = 13 \text{ ( remainder is } \color{blue}{ 0 } \text{ ) } $$

The remainder is zero => GCD is the last divisor $ \color{blue}{ \boxed { 15 }} $.

This solution can be visualized using a Venn diagram.

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

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