Step 1 :
Divide $ 10500 $ by $ 1260 $ and get the remainder

$$ 10500 : 1260 = 8 \text{ ( remainder is } \color{blue}{ 420 } \text{ ) } $$

The remainder is positive ($ 420 > 0 $), so we will continue with division.

Step 2 :
Divide $ 1260 $ by $ \color{blue}{ 420 } $ and get the remainder

$$ 1260 : \color{blue}{ \boxed { 420 }} = 3 \text{ ( remainder is } \color{blue}{ 0 } \text{ ) } $$

The remainder is zero => GCD is the last divisor $ \color{blue}{ \boxed { 420 }} $.

This solution can be visualized using a Venn diagram.

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

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