Step 1 :
Divide $ 298 $ by $ 31 $ and get the remainder

$$ 298 : 31 = 9 \text{ ( remainder is } \color{blue}{ 19 } \text{ ) } $$

The remainder is positive ($ 19 > 0 $), so we will continue with division.

Step 2 :
Divide $ 31 $ by $ \color{blue}{ 19 } $ and get the remainder

$$ 31 : 19 = 1 \text{ ( remainder is } \color{blue}{ 12 } \text{ ) } $$

The remainder is still positive ($ 12 > 0 $), so we will continue with division.

Step 3 :
Divide $ 19 $ by $ \color{blue}{ 12 } $ and get the remainder

$$ 19 : 12 = 1 \text{ ( remainder is } \color{blue}{ 7 } \text{ ) } $$

The remainder is still positive ($ 7 > 0 $), so we will continue with division.

Step 4 :
Divide $ 12 $ by $ \color{blue}{ 7 } $ and get the remainder

$$ 12 : 7 = 1 \text{ ( remainder is } \color{blue}{ 5 } \text{ ) } $$

The remainder is still positive ($ 5 > 0 $), so we will continue with division.

Step 5 :
Divide $ 7 $ by $ \color{blue}{ 5 } $ and get the remainder

$$ 7 : 5 = 1 \text{ ( remainder is } \color{blue}{ 2 } \text{ ) } $$

The remainder is still positive ($ 2 > 0 $), so we will continue with division.

Step 6 :
Divide $ 5 $ by $ \color{blue}{ 2 } $ and get the remainder

$$ 5 : 2 = 2 \text{ ( remainder is } \color{blue}{ 1 } \text{ ) } $$

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

Step 7 :
Divide $ 2 $ by $ \color{blue}{ 1 } $ and get the remainder

$$ 2 : \color{blue}{ \boxed { 1 }} = 2 \text{ ( remainder is } \color{blue}{ 0 } \text{ ) } $$

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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