Step 1 :
Divide $ 83159 $ by $ 78910 $ and get the remainder

$$ 83159 : 78910 = 1 \text{ ( remainder is } \color{blue}{ 4249 } \text{ ) } $$

The remainder is positive ($ 4249 > 0 $), so we will continue with division.

Step 2 :
Divide $ 78910 $ by $ \color{blue}{ 4249 } $ and get the remainder

$$ 78910 : 4249 = 18 \text{ ( remainder is } \color{blue}{ 2428 } \text{ ) } $$

The remainder is still positive ($ 2428 > 0 $), so we will continue with division.

Step 3 :
Divide $ 4249 $ by $ \color{blue}{ 2428 } $ and get the remainder

$$ 4249 : 2428 = 1 \text{ ( remainder is } \color{blue}{ 1821 } \text{ ) } $$

The remainder is still positive ($ 1821 > 0 $), so we will continue with division.

Step 4 :
Divide $ 2428 $ by $ \color{blue}{ 1821 } $ and get the remainder

$$ 2428 : 1821 = 1 \text{ ( remainder is } \color{blue}{ 607 } \text{ ) } $$

The remainder is still positive ($ 607 > 0 $), so we will continue with division.

Step 5 :
Divide $ 1821 $ by $ \color{blue}{ 607 } $ and get the remainder

$$ 1821 : \color{blue}{ \boxed { 607 }} = 3 \text{ ( remainder is } \color{blue}{ 0 } \text{ ) } $$

The remainder is zero => GCD is the last divisor $ \color{blue}{ \boxed { 607 }} $.

This solution can be visualized using a Venn diagram.

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

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