Step 1 :
Divide $ 889079 $ by $ 798215 $ and get the remainder

$$ 889079 : 798215 = 1 \text{ ( remainder is } \color{blue}{ 90864 } \text{ ) } $$

The remainder is positive ($ 90864 > 0 $), so we will continue with division.

Step 2 :
Divide $ 798215 $ by $ \color{blue}{ 90864 } $ and get the remainder

$$ 798215 : 90864 = 8 \text{ ( remainder is } \color{blue}{ 71303 } \text{ ) } $$

The remainder is still positive ($ 71303 > 0 $), so we will continue with division.

Step 3 :
Divide $ 90864 $ by $ \color{blue}{ 71303 } $ and get the remainder

$$ 90864 : 71303 = 1 \text{ ( remainder is } \color{blue}{ 19561 } \text{ ) } $$

The remainder is still positive ($ 19561 > 0 $), so we will continue with division.

Step 4 :
Divide $ 71303 $ by $ \color{blue}{ 19561 } $ and get the remainder

$$ 71303 : 19561 = 3 \text{ ( remainder is } \color{blue}{ 12620 } \text{ ) } $$

The remainder is still positive ($ 12620 > 0 $), so we will continue with division.

Step 5 :
Divide $ 19561 $ by $ \color{blue}{ 12620 } $ and get the remainder

$$ 19561 : 12620 = 1 \text{ ( remainder is } \color{blue}{ 6941 } \text{ ) } $$

The remainder is still positive ($ 6941 > 0 $), so we will continue with division.

Step 6 :
Divide $ 12620 $ by $ \color{blue}{ 6941 } $ and get the remainder

$$ 12620 : 6941 = 1 \text{ ( remainder is } \color{blue}{ 5679 } \text{ ) } $$

The remainder is still positive ($ 5679 > 0 $), so we will continue with division.

Step 7 :
Divide $ 6941 $ by $ \color{blue}{ 5679 } $ and get the remainder

$$ 6941 : 5679 = 1 \text{ ( remainder is } \color{blue}{ 1262 } \text{ ) } $$

The remainder is still positive ($ 1262 > 0 $), so we will continue with division.

Step 8 :
Divide $ 5679 $ by $ \color{blue}{ 1262 } $ and get the remainder

$$ 5679 : 1262 = 4 \text{ ( remainder is } \color{blue}{ 631 } \text{ ) } $$

The remainder is still positive ($ 631 > 0 $), so we will continue with division.

Step 9 :
Divide $ 1262 $ by $ \color{blue}{ 631 } $ and get the remainder

$$ 1262 : \color{blue}{ \boxed { 631 }} = 2 \text{ ( remainder is } \color{blue}{ 0 } \text{ ) } $$

The remainder is zero => GCD is the last divisor $ \color{blue}{ \boxed { 631 }} $.

This solution can be visualized using a Venn diagram.

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

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