Step 1 :
Divide $ 10256 $ by $ 5420 $ and get the remainder

$$ 10256 : 5420 = 1 \text{ ( remainder is } \color{blue}{ 4836 } \text{ ) } $$

The remainder is positive ($ 4836 > 0 $), so we will continue with division.

Step 2 :
Divide $ 5420 $ by $ \color{blue}{ 4836 } $ and get the remainder

$$ 5420 : 4836 = 1 \text{ ( remainder is } \color{blue}{ 584 } \text{ ) } $$

The remainder is still positive ($ 584 > 0 $), so we will continue with division.

Step 3 :
Divide $ 4836 $ by $ \color{blue}{ 584 } $ and get the remainder

$$ 4836 : 584 = 8 \text{ ( remainder is } \color{blue}{ 164 } \text{ ) } $$

The remainder is still positive ($ 164 > 0 $), so we will continue with division.

Step 4 :
Divide $ 584 $ by $ \color{blue}{ 164 } $ and get the remainder

$$ 584 : 164 = 3 \text{ ( remainder is } \color{blue}{ 92 } \text{ ) } $$

The remainder is still positive ($ 92 > 0 $), so we will continue with division.

Step 5 :
Divide $ 164 $ by $ \color{blue}{ 92 } $ and get the remainder

$$ 164 : 92 = 1 \text{ ( remainder is } \color{blue}{ 72 } \text{ ) } $$

The remainder is still positive ($ 72 > 0 $), so we will continue with division.

Step 6 :
Divide $ 92 $ by $ \color{blue}{ 72 } $ and get the remainder

$$ 92 : 72 = 1 \text{ ( remainder is } \color{blue}{ 20 } \text{ ) } $$

The remainder is still positive ($ 20 > 0 $), so we will continue with division.

Step 7 :
Divide $ 72 $ by $ \color{blue}{ 20 } $ and get the remainder

$$ 72 : 20 = 3 \text{ ( remainder is } \color{blue}{ 12 } \text{ ) } $$

The remainder is still positive ($ 12 > 0 $), so we will continue with division.

Step 8 :
Divide $ 20 $ by $ \color{blue}{ 12 } $ and get the remainder

$$ 20 : 12 = 1 \text{ ( remainder is } \color{blue}{ 8 } \text{ ) } $$

The remainder is still positive ($ 8 > 0 $), so we will continue with division.

Step 9 :
Divide $ 12 $ by $ \color{blue}{ 8 } $ and get the remainder

$$ 12 : 8 = 1 \text{ ( remainder is } \color{blue}{ 4 } \text{ ) } $$

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

Step 10 :
Divide $ 8 $ by $ \color{blue}{ 4 } $ and get the remainder

$$ 8 : \color{blue}{ \boxed { 4 }} = 2 \text{ ( remainder is } \color{blue}{ 0 } \text{ ) } $$

The remainder is zero => GCD is the last divisor $ \color{blue}{ \boxed { 4 }} $.

This solution can be visualized using a Venn diagram.

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

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