Step 1 :
Divide $ 120000 $ by $ 43242 $ and get the remainder

$$ 120000 : 43242 = 2 \text{ ( remainder is } \color{blue}{ 33516 } \text{ ) } $$

The remainder is positive ($ 33516 > 0 $), so we will continue with division.

Step 2 :
Divide $ 43242 $ by $ \color{blue}{ 33516 } $ and get the remainder

$$ 43242 : 33516 = 1 \text{ ( remainder is } \color{blue}{ 9726 } \text{ ) } $$

The remainder is still positive ($ 9726 > 0 $), so we will continue with division.

Step 3 :
Divide $ 33516 $ by $ \color{blue}{ 9726 } $ and get the remainder

$$ 33516 : 9726 = 3 \text{ ( remainder is } \color{blue}{ 4338 } \text{ ) } $$

The remainder is still positive ($ 4338 > 0 $), so we will continue with division.

Step 4 :
Divide $ 9726 $ by $ \color{blue}{ 4338 } $ and get the remainder

$$ 9726 : 4338 = 2 \text{ ( remainder is } \color{blue}{ 1050 } \text{ ) } $$

The remainder is still positive ($ 1050 > 0 $), so we will continue with division.

Step 5 :
Divide $ 4338 $ by $ \color{blue}{ 1050 } $ and get the remainder

$$ 4338 : 1050 = 4 \text{ ( remainder is } \color{blue}{ 138 } \text{ ) } $$

The remainder is still positive ($ 138 > 0 $), so we will continue with division.

Step 6 :
Divide $ 1050 $ by $ \color{blue}{ 138 } $ and get the remainder

$$ 1050 : 138 = 7 \text{ ( remainder is } \color{blue}{ 84 } \text{ ) } $$

The remainder is still positive ($ 84 > 0 $), so we will continue with division.

Step 7 :
Divide $ 138 $ by $ \color{blue}{ 84 } $ and get the remainder

$$ 138 : 84 = 1 \text{ ( remainder is } \color{blue}{ 54 } \text{ ) } $$

The remainder is still positive ($ 54 > 0 $), so we will continue with division.

Step 8 :
Divide $ 84 $ by $ \color{blue}{ 54 } $ and get the remainder

$$ 84 : 54 = 1 \text{ ( remainder is } \color{blue}{ 30 } \text{ ) } $$

The remainder is still positive ($ 30 > 0 $), so we will continue with division.

Step 9 :
Divide $ 54 $ by $ \color{blue}{ 30 } $ and get the remainder

$$ 54 : 30 = 1 \text{ ( remainder is } \color{blue}{ 24 } \text{ ) } $$

The remainder is still positive ($ 24 > 0 $), so we will continue with division.

Step 10 :
Divide $ 30 $ by $ \color{blue}{ 24 } $ and get the remainder

$$ 30 : 24 = 1 \text{ ( remainder is } \color{blue}{ 6 } \text{ ) } $$

The remainder is still positive ($ 6 > 0 $), so we will continue with division.

Step 11 :
Divide $ 24 $ by $ \color{blue}{ 6 } $ and get the remainder

$$ 24 : \color{blue}{ \boxed { 6 }} = 4 \text{ ( remainder is } \color{blue}{ 0 } \text{ ) } $$

The remainder is zero => GCD is the last divisor $ \color{blue}{ \boxed { 6 }} $.

This solution can be visualized using a Venn diagram.

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

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