Step 1 :
Divide $ 31145 $ by $ 11442 $ and get the remainder

$$ 31145 : 11442 = 2 \text{ ( remainder is } \color{blue}{ 8261 } \text{ ) } $$

The remainder is positive ($ 8261 > 0 $), so we will continue with division.

Step 2 :
Divide $ 11442 $ by $ \color{blue}{ 8261 } $ and get the remainder

$$ 11442 : 8261 = 1 \text{ ( remainder is } \color{blue}{ 3181 } \text{ ) } $$

The remainder is still positive ($ 3181 > 0 $), so we will continue with division.

Step 3 :
Divide $ 8261 $ by $ \color{blue}{ 3181 } $ and get the remainder

$$ 8261 : 3181 = 2 \text{ ( remainder is } \color{blue}{ 1899 } \text{ ) } $$

The remainder is still positive ($ 1899 > 0 $), so we will continue with division.

Step 4 :
Divide $ 3181 $ by $ \color{blue}{ 1899 } $ and get the remainder

$$ 3181 : 1899 = 1 \text{ ( remainder is } \color{blue}{ 1282 } \text{ ) } $$

The remainder is still positive ($ 1282 > 0 $), so we will continue with division.

Step 5 :
Divide $ 1899 $ by $ \color{blue}{ 1282 } $ and get the remainder

$$ 1899 : 1282 = 1 \text{ ( remainder is } \color{blue}{ 617 } \text{ ) } $$

The remainder is still positive ($ 617 > 0 $), so we will continue with division.

Step 6 :
Divide $ 1282 $ by $ \color{blue}{ 617 } $ and get the remainder

$$ 1282 : 617 = 2 \text{ ( remainder is } \color{blue}{ 48 } \text{ ) } $$

The remainder is still positive ($ 48 > 0 $), so we will continue with division.

Step 7 :
Divide $ 617 $ by $ \color{blue}{ 48 } $ and get the remainder

$$ 617 : 48 = 12 \text{ ( remainder is } \color{blue}{ 41 } \text{ ) } $$

The remainder is still positive ($ 41 > 0 $), so we will continue with division.

Step 8 :
Divide $ 48 $ by $ \color{blue}{ 41 } $ and get the remainder

$$ 48 : 41 = 1 \text{ ( remainder is } \color{blue}{ 7 } \text{ ) } $$

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

Step 9 :
Divide $ 41 $ by $ \color{blue}{ 7 } $ and get the remainder

$$ 41 : 7 = 5 \text{ ( remainder is } \color{blue}{ 6 } \text{ ) } $$

The remainder is still positive ($ 6 > 0 $), so we will continue with division.

Step 10 :
Divide $ 7 $ by $ \color{blue}{ 6 } $ and get the remainder

$$ 7 : 6 = 1 \text{ ( remainder is } \color{blue}{ 1 } \text{ ) } $$

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

Step 11 :
Divide $ 6 $ by $ \color{blue}{ 1 } $ and get the remainder

$$ 6 : \color{blue}{ \boxed { 1 }} = 6 \text{ ( remainder is } \color{blue}{ 0 } \text{ ) } $$

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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