Step 1 :
Divide $ 6999034 $ by $ 699111 $ and get the remainder

$$ 6999034 : 699111 = 10 \text{ ( remainder is } \color{blue}{ 7924 } \text{ ) } $$

The remainder is positive ($ 7924 > 0 $), so we will continue with division.

Step 2 :
Divide $ 699111 $ by $ \color{blue}{ 7924 } $ and get the remainder

$$ 699111 : 7924 = 88 \text{ ( remainder is } \color{blue}{ 1799 } \text{ ) } $$

The remainder is still positive ($ 1799 > 0 $), so we will continue with division.

Step 3 :
Divide $ 7924 $ by $ \color{blue}{ 1799 } $ and get the remainder

$$ 7924 : 1799 = 4 \text{ ( remainder is } \color{blue}{ 728 } \text{ ) } $$

The remainder is still positive ($ 728 > 0 $), so we will continue with division.

Step 4 :
Divide $ 1799 $ by $ \color{blue}{ 728 } $ and get the remainder

$$ 1799 : 728 = 2 \text{ ( remainder is } \color{blue}{ 343 } \text{ ) } $$

The remainder is still positive ($ 343 > 0 $), so we will continue with division.

Step 5 :
Divide $ 728 $ by $ \color{blue}{ 343 } $ and get the remainder

$$ 728 : 343 = 2 \text{ ( remainder is } \color{blue}{ 42 } \text{ ) } $$

The remainder is still positive ($ 42 > 0 $), so we will continue with division.

Step 6 :
Divide $ 343 $ by $ \color{blue}{ 42 } $ and get the remainder

$$ 343 : 42 = 8 \text{ ( remainder is } \color{blue}{ 7 } \text{ ) } $$

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

Step 7 :
Divide $ 42 $ by $ \color{blue}{ 7 } $ and get the remainder

$$ 42 : \color{blue}{ \boxed { 7 }} = 6 \text{ ( remainder is } \color{blue}{ 0 } \text{ ) } $$

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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