Step 1 :
Divide $ 24486 $ by $ 14828 $ and get the remainder

$$ 24486 : 14828 = 1 \text{ ( remainder is } \color{blue}{ 9658 } \text{ ) } $$

The remainder is positive ($ 9658 > 0 $), so we will continue with division.

Step 2 :
Divide $ 14828 $ by $ \color{blue}{ 9658 } $ and get the remainder

$$ 14828 : 9658 = 1 \text{ ( remainder is } \color{blue}{ 5170 } \text{ ) } $$

The remainder is still positive ($ 5170 > 0 $), so we will continue with division.

Step 3 :
Divide $ 9658 $ by $ \color{blue}{ 5170 } $ and get the remainder

$$ 9658 : 5170 = 1 \text{ ( remainder is } \color{blue}{ 4488 } \text{ ) } $$

The remainder is still positive ($ 4488 > 0 $), so we will continue with division.

Step 4 :
Divide $ 5170 $ by $ \color{blue}{ 4488 } $ and get the remainder

$$ 5170 : 4488 = 1 \text{ ( remainder is } \color{blue}{ 682 } \text{ ) } $$

The remainder is still positive ($ 682 > 0 $), so we will continue with division.

Step 5 :
Divide $ 4488 $ by $ \color{blue}{ 682 } $ and get the remainder

$$ 4488 : 682 = 6 \text{ ( remainder is } \color{blue}{ 396 } \text{ ) } $$

The remainder is still positive ($ 396 > 0 $), so we will continue with division.

Step 6 :
Divide $ 682 $ by $ \color{blue}{ 396 } $ and get the remainder

$$ 682 : 396 = 1 \text{ ( remainder is } \color{blue}{ 286 } \text{ ) } $$

The remainder is still positive ($ 286 > 0 $), so we will continue with division.

Step 7 :
Divide $ 396 $ by $ \color{blue}{ 286 } $ and get the remainder

$$ 396 : 286 = 1 \text{ ( remainder is } \color{blue}{ 110 } \text{ ) } $$

The remainder is still positive ($ 110 > 0 $), so we will continue with division.

Step 8 :
Divide $ 286 $ by $ \color{blue}{ 110 } $ and get the remainder

$$ 286 : 110 = 2 \text{ ( remainder is } \color{blue}{ 66 } \text{ ) } $$

The remainder is still positive ($ 66 > 0 $), so we will continue with division.

Step 9 :
Divide $ 110 $ by $ \color{blue}{ 66 } $ and get the remainder

$$ 110 : 66 = 1 \text{ ( remainder is } \color{blue}{ 44 } \text{ ) } $$

The remainder is still positive ($ 44 > 0 $), so we will continue with division.

Step 10 :
Divide $ 66 $ by $ \color{blue}{ 44 } $ and get the remainder

$$ 66 : 44 = 1 \text{ ( remainder is } \color{blue}{ 22 } \text{ ) } $$

The remainder is still positive ($ 22 > 0 $), so we will continue with division.

Step 11 :
Divide $ 44 $ by $ \color{blue}{ 22 } $ and get the remainder

$$ 44 : \color{blue}{ \boxed { 22 }} = 2 \text{ ( remainder is } \color{blue}{ 0 } \text{ ) } $$

The remainder is zero => GCD is the last divisor $ \color{blue}{ \boxed { 22 }} $.

This solution can be visualized using a Venn diagram.

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

GCD Calculator