Step 1 :
Divide $ 42828 $ by $ 6409 $ and get the remainder

$$ 42828 : 6409 = 6 \text{ ( remainder is } \color{blue}{ 4374 } \text{ ) } $$

The remainder is positive ($ 4374 > 0 $), so we will continue with division.

Step 2 :
Divide $ 6409 $ by $ \color{blue}{ 4374 } $ and get the remainder

$$ 6409 : 4374 = 1 \text{ ( remainder is } \color{blue}{ 2035 } \text{ ) } $$

The remainder is still positive ($ 2035 > 0 $), so we will continue with division.

Step 3 :
Divide $ 4374 $ by $ \color{blue}{ 2035 } $ and get the remainder

$$ 4374 : 2035 = 2 \text{ ( remainder is } \color{blue}{ 304 } \text{ ) } $$

The remainder is still positive ($ 304 > 0 $), so we will continue with division.

Step 4 :
Divide $ 2035 $ by $ \color{blue}{ 304 } $ and get the remainder

$$ 2035 : 304 = 6 \text{ ( remainder is } \color{blue}{ 211 } \text{ ) } $$

The remainder is still positive ($ 211 > 0 $), so we will continue with division.

Step 5 :
Divide $ 304 $ by $ \color{blue}{ 211 } $ and get the remainder

$$ 304 : 211 = 1 \text{ ( remainder is } \color{blue}{ 93 } \text{ ) } $$

The remainder is still positive ($ 93 > 0 $), so we will continue with division.

Step 6 :
Divide $ 211 $ by $ \color{blue}{ 93 } $ and get the remainder

$$ 211 : 93 = 2 \text{ ( remainder is } \color{blue}{ 25 } \text{ ) } $$

The remainder is still positive ($ 25 > 0 $), so we will continue with division.

Step 7 :
Divide $ 93 $ by $ \color{blue}{ 25 } $ and get the remainder

$$ 93 : 25 = 3 \text{ ( remainder is } \color{blue}{ 18 } \text{ ) } $$

The remainder is still positive ($ 18 > 0 $), so we will continue with division.

Step 8 :
Divide $ 25 $ by $ \color{blue}{ 18 } $ and get the remainder

$$ 25 : 18 = 1 \text{ ( remainder is } \color{blue}{ 7 } \text{ ) } $$

The remainder is still positive ($ 7 > 0 $), so we will continue with division.

Step 9 :
Divide $ 18 $ by $ \color{blue}{ 7 } $ and get the remainder

$$ 18 : 7 = 2 \text{ ( remainder is } \color{blue}{ 4 } \text{ ) } $$

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

Step 10 :
Divide $ 7 $ by $ \color{blue}{ 4 } $ and get the remainder

$$ 7 : 4 = 1 \text{ ( remainder is } \color{blue}{ 3 } \text{ ) } $$

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

Step 11 :
Divide $ 4 $ by $ \color{blue}{ 3 } $ and get the remainder

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

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

Step 12 :
Divide $ 3 $ by $ \color{blue}{ 1 } $ and get the remainder

$$ 3 : \color{blue}{ \boxed { 1 }} = 3 \text{ ( remainder is } \color{blue}{ 0 } \text{ ) } $$

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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