Step 1 :
Divide $ 32842 $ by $ 5928 $ and get the remainder

$$ 32842 : 5928 = 5 \text{ ( remainder is } \color{blue}{ 3202 } \text{ ) } $$

The remainder is positive ($ 3202 > 0 $), so we will continue with division.

Step 2 :
Divide $ 5928 $ by $ \color{blue}{ 3202 } $ and get the remainder

$$ 5928 : 3202 = 1 \text{ ( remainder is } \color{blue}{ 2726 } \text{ ) } $$

The remainder is still positive ($ 2726 > 0 $), so we will continue with division.

Step 3 :
Divide $ 3202 $ by $ \color{blue}{ 2726 } $ and get the remainder

$$ 3202 : 2726 = 1 \text{ ( remainder is } \color{blue}{ 476 } \text{ ) } $$

The remainder is still positive ($ 476 > 0 $), so we will continue with division.

Step 4 :
Divide $ 2726 $ by $ \color{blue}{ 476 } $ and get the remainder

$$ 2726 : 476 = 5 \text{ ( remainder is } \color{blue}{ 346 } \text{ ) } $$

The remainder is still positive ($ 346 > 0 $), so we will continue with division.

Step 5 :
Divide $ 476 $ by $ \color{blue}{ 346 } $ and get the remainder

$$ 476 : 346 = 1 \text{ ( remainder is } \color{blue}{ 130 } \text{ ) } $$

The remainder is still positive ($ 130 > 0 $), so we will continue with division.

Step 6 :
Divide $ 346 $ by $ \color{blue}{ 130 } $ and get the remainder

$$ 346 : 130 = 2 \text{ ( remainder is } \color{blue}{ 86 } \text{ ) } $$

The remainder is still positive ($ 86 > 0 $), so we will continue with division.

Step 7 :
Divide $ 130 $ by $ \color{blue}{ 86 } $ and get the remainder

$$ 130 : 86 = 1 \text{ ( remainder is } \color{blue}{ 44 } \text{ ) } $$

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

Step 8 :
Divide $ 86 $ by $ \color{blue}{ 44 } $ and get the remainder

$$ 86 : 44 = 1 \text{ ( remainder is } \color{blue}{ 42 } \text{ ) } $$

The remainder is still positive ($ 42 > 0 $), so we will continue with division.

Step 9 :
Divide $ 44 $ by $ \color{blue}{ 42 } $ and get the remainder

$$ 44 : 42 = 1 \text{ ( remainder is } \color{blue}{ 2 } \text{ ) } $$

The remainder is still positive ($ 2 > 0 $), so we will continue with division.

Step 10 :
Divide $ 42 $ by $ \color{blue}{ 2 } $ and get the remainder

$$ 42 : \color{blue}{ \boxed { 2 }} = 21 \text{ ( remainder is } \color{blue}{ 0 } \text{ ) } $$

The remainder is zero => GCD is the last divisor $ \color{blue}{ \boxed { 2 }} $.

This solution can be visualized using a Venn diagram.

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

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