Step 1 :
Divide $ 8051 $ by $ 4635 $ and get the remainder

$$ 8051 : 4635 = 1 \text{ ( remainder is } \color{blue}{ 3416 } \text{ ) } $$

The remainder is positive ($ 3416 > 0 $), so we will continue with division.

Step 2 :
Divide $ 4635 $ by $ \color{blue}{ 3416 } $ and get the remainder

$$ 4635 : 3416 = 1 \text{ ( remainder is } \color{blue}{ 1219 } \text{ ) } $$

The remainder is still positive ($ 1219 > 0 $), so we will continue with division.

Step 3 :
Divide $ 3416 $ by $ \color{blue}{ 1219 } $ and get the remainder

$$ 3416 : 1219 = 2 \text{ ( remainder is } \color{blue}{ 978 } \text{ ) } $$

The remainder is still positive ($ 978 > 0 $), so we will continue with division.

Step 4 :
Divide $ 1219 $ by $ \color{blue}{ 978 } $ and get the remainder

$$ 1219 : 978 = 1 \text{ ( remainder is } \color{blue}{ 241 } \text{ ) } $$

The remainder is still positive ($ 241 > 0 $), so we will continue with division.

Step 5 :
Divide $ 978 $ by $ \color{blue}{ 241 } $ and get the remainder

$$ 978 : 241 = 4 \text{ ( remainder is } \color{blue}{ 14 } \text{ ) } $$

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

Step 6 :
Divide $ 241 $ by $ \color{blue}{ 14 } $ and get the remainder

$$ 241 : 14 = 17 \text{ ( remainder is } \color{blue}{ 3 } \text{ ) } $$

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

Step 7 :
Divide $ 14 $ by $ \color{blue}{ 3 } $ and get the remainder

$$ 14 : 3 = 4 \text{ ( remainder is } \color{blue}{ 2 } \text{ ) } $$

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

Step 8 :
Divide $ 3 $ by $ \color{blue}{ 2 } $ and get the remainder

$$ 3 : 2 = 1 \text{ ( remainder is } \color{blue}{ 1 } \text{ ) } $$

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

Step 9 :
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.

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