Step 1 :
Divide $ 899 $ by $ 688 $ and get the remainder

$$ 899 : 688 = 1 \text{ ( remainder is } \color{blue}{ 211 } \text{ ) } $$

The remainder is positive ($ 211 > 0 $), so we will continue with division.

Step 2 :
Divide $ 688 $ by $ \color{blue}{ 211 } $ and get the remainder

$$ 688 : 211 = 3 \text{ ( remainder is } \color{blue}{ 55 } \text{ ) } $$

The remainder is still positive ($ 55 > 0 $), so we will continue with division.

Step 3 :
Divide $ 211 $ by $ \color{blue}{ 55 } $ and get the remainder

$$ 211 : 55 = 3 \text{ ( remainder is } \color{blue}{ 46 } \text{ ) } $$

The remainder is still positive ($ 46 > 0 $), so we will continue with division.

Step 4 :
Divide $ 55 $ by $ \color{blue}{ 46 } $ and get the remainder

$$ 55 : 46 = 1 \text{ ( remainder is } \color{blue}{ 9 } \text{ ) } $$

The remainder is still positive ($ 9 > 0 $), so we will continue with division.

Step 5 :
Divide $ 46 $ by $ \color{blue}{ 9 } $ and get the remainder

$$ 46 : 9 = 5 \text{ ( remainder is } \color{blue}{ 1 } \text{ ) } $$

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

Step 6 :
Divide $ 9 $ by $ \color{blue}{ 1 } $ and get the remainder

$$ 9 : \color{blue}{ \boxed { 1 }} = 9 \text{ ( remainder is } \color{blue}{ 0 } \text{ ) } $$

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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