Step 1 :
Divide $ 2561124 $ by $ 46064 $ and get the remainder

$$ 2561124 : 46064 = 55 \text{ ( remainder is } \color{blue}{ 27604 } \text{ ) } $$

The remainder is positive ($ 27604 > 0 $), so we will continue with division.

Step 2 :
Divide $ 46064 $ by $ \color{blue}{ 27604 } $ and get the remainder

$$ 46064 : 27604 = 1 \text{ ( remainder is } \color{blue}{ 18460 } \text{ ) } $$

The remainder is still positive ($ 18460 > 0 $), so we will continue with division.

Step 3 :
Divide $ 27604 $ by $ \color{blue}{ 18460 } $ and get the remainder

$$ 27604 : 18460 = 1 \text{ ( remainder is } \color{blue}{ 9144 } \text{ ) } $$

The remainder is still positive ($ 9144 > 0 $), so we will continue with division.

Step 4 :
Divide $ 18460 $ by $ \color{blue}{ 9144 } $ and get the remainder

$$ 18460 : 9144 = 2 \text{ ( remainder is } \color{blue}{ 172 } \text{ ) } $$

The remainder is still positive ($ 172 > 0 $), so we will continue with division.

Step 5 :
Divide $ 9144 $ by $ \color{blue}{ 172 } $ and get the remainder

$$ 9144 : 172 = 53 \text{ ( remainder is } \color{blue}{ 28 } \text{ ) } $$

The remainder is still positive ($ 28 > 0 $), so we will continue with division.

Step 6 :
Divide $ 172 $ by $ \color{blue}{ 28 } $ and get the remainder

$$ 172 : 28 = 6 \text{ ( remainder is } \color{blue}{ 4 } \text{ ) } $$

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

Step 7 :
Divide $ 28 $ by $ \color{blue}{ 4 } $ and get the remainder

$$ 28 : \color{blue}{ \boxed { 4 }} = 7 \text{ ( remainder is } \color{blue}{ 0 } \text{ ) } $$

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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