Step 1 :
Divide $ 924 $ by $ 647 $ and get the remainder

$$ 924 : 647 = 1 \text{ ( remainder is } \color{blue}{ 277 } \text{ ) } $$

The remainder is positive ($ 277 > 0 $), so we will continue with division.

Step 2 :
Divide $ 647 $ by $ \color{blue}{ 277 } $ and get the remainder

$$ 647 : 277 = 2 \text{ ( remainder is } \color{blue}{ 93 } \text{ ) } $$

The remainder is still positive ($ 93 > 0 $), so we will continue with division.

Step 3 :
Divide $ 277 $ by $ \color{blue}{ 93 } $ and get the remainder

$$ 277 : 93 = 2 \text{ ( remainder is } \color{blue}{ 91 } \text{ ) } $$

The remainder is still positive ($ 91 > 0 $), so we will continue with division.

Step 4 :
Divide $ 93 $ by $ \color{blue}{ 91 } $ and get the remainder

$$ 93 : 91 = 1 \text{ ( remainder is } \color{blue}{ 2 } \text{ ) } $$

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

Step 5 :
Divide $ 91 $ by $ \color{blue}{ 2 } $ and get the remainder

$$ 91 : 2 = 45 \text{ ( remainder is } \color{blue}{ 1 } \text{ ) } $$

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

Step 6 :
Divide $ 2 $ by $ \color{blue}{ 1 } $ and get the remainder

$$ 2 : \color{blue}{ \boxed { 1 }} = 2 \text{ ( remainder is } \color{blue}{ 0 } \text{ ) } $$

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.

GCD Calculator