Step 1 :
Divide $ 700 $ by $ 401 $ and get the remainder

$$ 700 : 401 = 1 \text{ ( remainder is } \color{blue}{ 299 } \text{ ) } $$

The remainder is positive ($ 299 > 0 $), so we will continue with division.

Step 2 :
Divide $ 401 $ by $ \color{blue}{ 299 } $ and get the remainder

$$ 401 : 299 = 1 \text{ ( remainder is } \color{blue}{ 102 } \text{ ) } $$

The remainder is still positive ($ 102 > 0 $), so we will continue with division.

Step 3 :
Divide $ 299 $ by $ \color{blue}{ 102 } $ and get the remainder

$$ 299 : 102 = 2 \text{ ( remainder is } \color{blue}{ 95 } \text{ ) } $$

The remainder is still positive ($ 95 > 0 $), so we will continue with division.

Step 4 :
Divide $ 102 $ by $ \color{blue}{ 95 } $ and get the remainder

$$ 102 : 95 = 1 \text{ ( remainder is } \color{blue}{ 7 } \text{ ) } $$

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

Step 5 :
Divide $ 95 $ by $ \color{blue}{ 7 } $ and get the remainder

$$ 95 : 7 = 13 \text{ ( remainder is } \color{blue}{ 4 } \text{ ) } $$

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

Step 6 :
Divide $ 7 $ by $ \color{blue}{ 4 } $ and get the remainder

$$ 7 : 4 = 1 \text{ ( remainder is } \color{blue}{ 3 } \text{ ) } $$

The remainder is still positive ($ 3 > 0 $), so we will continue with division.

Step 7 :
Divide $ 4 $ by $ \color{blue}{ 3 } $ and get the remainder

$$ 4 : 3 = 1 \text{ ( remainder is } \color{blue}{ 1 } \text{ ) } $$

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

Step 8 :
Divide $ 3 $ by $ \color{blue}{ 1 } $ and get the remainder

$$ 3 : \color{blue}{ \boxed { 1 }} = 3 \text{ ( remainder is } \color{blue}{ 0 } \text{ ) } $$

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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