Step 1 :
Divide $ 892 $ by $ 650 $ and get the remainder

$$ 892 : 650 = 1 \text{ ( remainder is } \color{blue}{ 242 } \text{ ) } $$

The remainder is positive ($ 242 > 0 $), so we will continue with division.

Step 2 :
Divide $ 650 $ by $ \color{blue}{ 242 } $ and get the remainder

$$ 650 : 242 = 2 \text{ ( remainder is } \color{blue}{ 166 } \text{ ) } $$

The remainder is still positive ($ 166 > 0 $), so we will continue with division.

Step 3 :
Divide $ 242 $ by $ \color{blue}{ 166 } $ and get the remainder

$$ 242 : 166 = 1 \text{ ( remainder is } \color{blue}{ 76 } \text{ ) } $$

The remainder is still positive ($ 76 > 0 $), so we will continue with division.

Step 4 :
Divide $ 166 $ by $ \color{blue}{ 76 } $ and get the remainder

$$ 166 : 76 = 2 \text{ ( remainder is } \color{blue}{ 14 } \text{ ) } $$

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

Step 5 :
Divide $ 76 $ by $ \color{blue}{ 14 } $ and get the remainder

$$ 76 : 14 = 5 \text{ ( remainder is } \color{blue}{ 6 } \text{ ) } $$

The remainder is still positive ($ 6 > 0 $), so we will continue with division.

Step 6 :
Divide $ 14 $ by $ \color{blue}{ 6 } $ and get the remainder

$$ 14 : 6 = 2 \text{ ( remainder is } \color{blue}{ 2 } \text{ ) } $$

The remainder is still positive ($ 2 > 0 $), so we will continue with division.

Step 7 :
Divide $ 6 $ by $ \color{blue}{ 2 } $ and get the remainder

$$ 6 : \color{blue}{ \boxed { 2 }} = 3 \text{ ( remainder is } \color{blue}{ 0 } \text{ ) } $$

The remainder is zero => GCD is the last divisor $ \color{blue}{ \boxed { 2 }} $.

This solution can be visualized using a Venn diagram.

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

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