Step 1 :
Divide $ 1251096 $ by $ 29249 $ and get the remainder

$$ 1251096 : 29249 = 42 \text{ ( remainder is } \color{blue}{ 22638 } \text{ ) } $$

The remainder is positive ($ 22638 > 0 $), so we will continue with division.

Step 2 :
Divide $ 29249 $ by $ \color{blue}{ 22638 } $ and get the remainder

$$ 29249 : 22638 = 1 \text{ ( remainder is } \color{blue}{ 6611 } \text{ ) } $$

The remainder is still positive ($ 6611 > 0 $), so we will continue with division.

Step 3 :
Divide $ 22638 $ by $ \color{blue}{ 6611 } $ and get the remainder

$$ 22638 : 6611 = 3 \text{ ( remainder is } \color{blue}{ 2805 } \text{ ) } $$

The remainder is still positive ($ 2805 > 0 $), so we will continue with division.

Step 4 :
Divide $ 6611 $ by $ \color{blue}{ 2805 } $ and get the remainder

$$ 6611 : 2805 = 2 \text{ ( remainder is } \color{blue}{ 1001 } \text{ ) } $$

The remainder is still positive ($ 1001 > 0 $), so we will continue with division.

Step 5 :
Divide $ 2805 $ by $ \color{blue}{ 1001 } $ and get the remainder

$$ 2805 : 1001 = 2 \text{ ( remainder is } \color{blue}{ 803 } \text{ ) } $$

The remainder is still positive ($ 803 > 0 $), so we will continue with division.

Step 6 :
Divide $ 1001 $ by $ \color{blue}{ 803 } $ and get the remainder

$$ 1001 : 803 = 1 \text{ ( remainder is } \color{blue}{ 198 } \text{ ) } $$

The remainder is still positive ($ 198 > 0 $), so we will continue with division.

Step 7 :
Divide $ 803 $ by $ \color{blue}{ 198 } $ and get the remainder

$$ 803 : 198 = 4 \text{ ( remainder is } \color{blue}{ 11 } \text{ ) } $$

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

Step 8 :
Divide $ 198 $ by $ \color{blue}{ 11 } $ and get the remainder

$$ 198 : \color{blue}{ \boxed { 11 }} = 18 \text{ ( remainder is } \color{blue}{ 0 } \text{ ) } $$

The remainder is zero => GCD is the last divisor $ \color{blue}{ \boxed { 11 }} $.

This solution can be visualized using a Venn diagram.

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

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