Step 1 :
Divide $ 889079 $ by $ 798216 $ and get the remainder

$$ 889079 : 798216 = 1 \text{ ( remainder is } \color{blue}{ 90863 } \text{ ) } $$

The remainder is positive ($ 90863 > 0 $), so we will continue with division.

Step 2 :
Divide $ 798216 $ by $ \color{blue}{ 90863 } $ and get the remainder

$$ 798216 : 90863 = 8 \text{ ( remainder is } \color{blue}{ 71312 } \text{ ) } $$

The remainder is still positive ($ 71312 > 0 $), so we will continue with division.

Step 3 :
Divide $ 90863 $ by $ \color{blue}{ 71312 } $ and get the remainder

$$ 90863 : 71312 = 1 \text{ ( remainder is } \color{blue}{ 19551 } \text{ ) } $$

The remainder is still positive ($ 19551 > 0 $), so we will continue with division.

Step 4 :
Divide $ 71312 $ by $ \color{blue}{ 19551 } $ and get the remainder

$$ 71312 : 19551 = 3 \text{ ( remainder is } \color{blue}{ 12659 } \text{ ) } $$

The remainder is still positive ($ 12659 > 0 $), so we will continue with division.

Step 5 :
Divide $ 19551 $ by $ \color{blue}{ 12659 } $ and get the remainder

$$ 19551 : 12659 = 1 \text{ ( remainder is } \color{blue}{ 6892 } \text{ ) } $$

The remainder is still positive ($ 6892 > 0 $), so we will continue with division.

Step 6 :
Divide $ 12659 $ by $ \color{blue}{ 6892 } $ and get the remainder

$$ 12659 : 6892 = 1 \text{ ( remainder is } \color{blue}{ 5767 } \text{ ) } $$

The remainder is still positive ($ 5767 > 0 $), so we will continue with division.

Step 7 :
Divide $ 6892 $ by $ \color{blue}{ 5767 } $ and get the remainder

$$ 6892 : 5767 = 1 \text{ ( remainder is } \color{blue}{ 1125 } \text{ ) } $$

The remainder is still positive ($ 1125 > 0 $), so we will continue with division.

Step 8 :
Divide $ 5767 $ by $ \color{blue}{ 1125 } $ and get the remainder

$$ 5767 : 1125 = 5 \text{ ( remainder is } \color{blue}{ 142 } \text{ ) } $$

The remainder is still positive ($ 142 > 0 $), so we will continue with division.

Step 9 :
Divide $ 1125 $ by $ \color{blue}{ 142 } $ and get the remainder

$$ 1125 : 142 = 7 \text{ ( remainder is } \color{blue}{ 131 } \text{ ) } $$

The remainder is still positive ($ 131 > 0 $), so we will continue with division.

Step 10 :
Divide $ 142 $ by $ \color{blue}{ 131 } $ and get the remainder

$$ 142 : 131 = 1 \text{ ( remainder is } \color{blue}{ 11 } \text{ ) } $$

The remainder is still positive ($ 11 > 0 $), so we will continue with division.

Step 11 :
Divide $ 131 $ by $ \color{blue}{ 11 } $ and get the remainder

$$ 131 : 11 = 11 \text{ ( remainder is } \color{blue}{ 10 } \text{ ) } $$

The remainder is still positive ($ 10 > 0 $), so we will continue with division.

Step 12 :
Divide $ 11 $ by $ \color{blue}{ 10 } $ and get the remainder

$$ 11 : 10 = 1 \text{ ( remainder is } \color{blue}{ 1 } \text{ ) } $$

The remainder is still positive ($ 1 > 0 $), so we will continue with division.

Step 13 :
Divide $ 10 $ by $ \color{blue}{ 1 } $ and get the remainder

$$ 10 : \color{blue}{ \boxed { 1 }} = 10 \text{ ( remainder is } \color{blue}{ 0 } \text{ ) } $$

The remainder is zero => GCD is the last divisor $ \color{blue}{ \boxed { 1 }} $.

This solution can be visualized using a Venn diagram.

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

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