Step 1 :
Divide $ 2579 $ by $ 2424 $ and get the remainder

$$ 2579 : 2424 = 1 \text{ ( remainder is } \color{blue}{ 155 } \text{ ) } $$

The remainder is positive ($ 155 > 0 $), so we will continue with division.

Step 2 :
Divide $ 2424 $ by $ \color{blue}{ 155 } $ and get the remainder

$$ 2424 : 155 = 15 \text{ ( remainder is } \color{blue}{ 99 } \text{ ) } $$

The remainder is still positive ($ 99 > 0 $), so we will continue with division.

Step 3 :
Divide $ 155 $ by $ \color{blue}{ 99 } $ and get the remainder

$$ 155 : 99 = 1 \text{ ( remainder is } \color{blue}{ 56 } \text{ ) } $$

The remainder is still positive ($ 56 > 0 $), so we will continue with division.

Step 4 :
Divide $ 99 $ by $ \color{blue}{ 56 } $ and get the remainder

$$ 99 : 56 = 1 \text{ ( remainder is } \color{blue}{ 43 } \text{ ) } $$

The remainder is still positive ($ 43 > 0 $), so we will continue with division.

Step 5 :
Divide $ 56 $ by $ \color{blue}{ 43 } $ and get the remainder

$$ 56 : 43 = 1 \text{ ( remainder is } \color{blue}{ 13 } \text{ ) } $$

The remainder is still positive ($ 13 > 0 $), so we will continue with division.

Step 6 :
Divide $ 43 $ by $ \color{blue}{ 13 } $ and get the remainder

$$ 43 : 13 = 3 \text{ ( remainder is } \color{blue}{ 4 } \text{ ) } $$

The remainder is still positive ($ 4 > 0 $), so we will continue with division.

Step 7 :
Divide $ 13 $ by $ \color{blue}{ 4 } $ and get the remainder

$$ 13 : 4 = 3 \text{ ( remainder is } \color{blue}{ 1 } \text{ ) } $$

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

Step 8 :
Divide $ 4 $ by $ \color{blue}{ 1 } $ and get the remainder

$$ 4 : \color{blue}{ \boxed { 1 }} = 4 \text{ ( remainder is } \color{blue}{ 0 } \text{ ) } $$

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