Step 1 :
Divide $ 1001 $ by $ 210 $ and get the remainder

$$ 1001 : 210 = 4 \text{ ( remainder is } \color{blue}{ 161 } \text{ ) } $$

The remainder is positive ($ 161 > 0 $), so we will continue with division.

Step 2 :
Divide $ 210 $ by $ \color{blue}{ 161 } $ and get the remainder

$$ 210 : 161 = 1 \text{ ( remainder is } \color{blue}{ 49 } \text{ ) } $$

The remainder is still positive ($ 49 > 0 $), so we will continue with division.

Step 3 :
Divide $ 161 $ by $ \color{blue}{ 49 } $ and get the remainder

$$ 161 : 49 = 3 \text{ ( remainder is } \color{blue}{ 14 } \text{ ) } $$

The remainder is still positive ($ 14 > 0 $), so we will continue with division.

Step 4 :
Divide $ 49 $ by $ \color{blue}{ 14 } $ and get the remainder

$$ 49 : 14 = 3 \text{ ( remainder is } \color{blue}{ 7 } \text{ ) } $$

The remainder is still positive ($ 7 > 0 $), so we will continue with division.

Step 5 :
Divide $ 14 $ by $ \color{blue}{ 7 } $ and get the remainder

$$ 14 : \color{blue}{ \boxed { 7 }} = 2 \text{ ( remainder is } \color{blue}{ 0 } \text{ ) } $$

The remainder is zero => GCD is the last divisor $ \color{blue}{ \boxed { 7 }} $.

This solution can be visualized using a Venn diagram.

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

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