Step 1 :
Divide $ 83159 $ by $ 78912 $ and get the remainder

$$ 83159 : 78912 = 1 \text{ ( remainder is } \color{blue}{ 4247 } \text{ ) } $$

The remainder is positive ($ 4247 > 0 $), so we will continue with division.

Step 2 :
Divide $ 78912 $ by $ \color{blue}{ 4247 } $ and get the remainder

$$ 78912 : 4247 = 18 \text{ ( remainder is } \color{blue}{ 2466 } \text{ ) } $$

The remainder is still positive ($ 2466 > 0 $), so we will continue with division.

Step 3 :
Divide $ 4247 $ by $ \color{blue}{ 2466 } $ and get the remainder

$$ 4247 : 2466 = 1 \text{ ( remainder is } \color{blue}{ 1781 } \text{ ) } $$

The remainder is still positive ($ 1781 > 0 $), so we will continue with division.

Step 4 :
Divide $ 2466 $ by $ \color{blue}{ 1781 } $ and get the remainder

$$ 2466 : 1781 = 1 \text{ ( remainder is } \color{blue}{ 685 } \text{ ) } $$

The remainder is still positive ($ 685 > 0 $), so we will continue with division.

Step 5 :
Divide $ 1781 $ by $ \color{blue}{ 685 } $ and get the remainder

$$ 1781 : 685 = 2 \text{ ( remainder is } \color{blue}{ 411 } \text{ ) } $$

The remainder is still positive ($ 411 > 0 $), so we will continue with division.

Step 6 :
Divide $ 685 $ by $ \color{blue}{ 411 } $ and get the remainder

$$ 685 : 411 = 1 \text{ ( remainder is } \color{blue}{ 274 } \text{ ) } $$

The remainder is still positive ($ 274 > 0 $), so we will continue with division.

Step 7 :
Divide $ 411 $ by $ \color{blue}{ 274 } $ and get the remainder

$$ 411 : 274 = 1 \text{ ( remainder is } \color{blue}{ 137 } \text{ ) } $$

The remainder is still positive ($ 137 > 0 $), so we will continue with division.

Step 8 :
Divide $ 274 $ by $ \color{blue}{ 137 } $ and get the remainder

$$ 274 : \color{blue}{ \boxed { 137 }} = 2 \text{ ( remainder is } \color{blue}{ 0 } \text{ ) } $$

The remainder is zero => GCD is the last divisor $ \color{blue}{ \boxed { 137 }} $.

This solution can be visualized using a Venn diagram.

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

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