Step 1 :
Divide $ 3149 $ by $ 2598 $ and get the remainder

$$ 3149 : 2598 = 1 \text{ ( remainder is } \color{blue}{ 551 } \text{ ) } $$

The remainder is positive ($ 551 > 0 $), so we will continue with division.

Step 2 :
Divide $ 2598 $ by $ \color{blue}{ 551 } $ and get the remainder

$$ 2598 : 551 = 4 \text{ ( remainder is } \color{blue}{ 394 } \text{ ) } $$

The remainder is still positive ($ 394 > 0 $), so we will continue with division.

Step 3 :
Divide $ 551 $ by $ \color{blue}{ 394 } $ and get the remainder

$$ 551 : 394 = 1 \text{ ( remainder is } \color{blue}{ 157 } \text{ ) } $$

The remainder is still positive ($ 157 > 0 $), so we will continue with division.

Step 4 :
Divide $ 394 $ by $ \color{blue}{ 157 } $ and get the remainder

$$ 394 : 157 = 2 \text{ ( remainder is } \color{blue}{ 80 } \text{ ) } $$

The remainder is still positive ($ 80 > 0 $), so we will continue with division.

Step 5 :
Divide $ 157 $ by $ \color{blue}{ 80 } $ and get the remainder

$$ 157 : 80 = 1 \text{ ( remainder is } \color{blue}{ 77 } \text{ ) } $$

The remainder is still positive ($ 77 > 0 $), so we will continue with division.

Step 6 :
Divide $ 80 $ by $ \color{blue}{ 77 } $ and get the remainder

$$ 80 : 77 = 1 \text{ ( remainder is } \color{blue}{ 3 } \text{ ) } $$

The remainder is still positive ($ 3 > 0 $), so we will continue with division.

Step 7 :
Divide $ 77 $ by $ \color{blue}{ 3 } $ and get the remainder

$$ 77 : 3 = 25 \text{ ( remainder is } \color{blue}{ 2 } \text{ ) } $$

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

Step 8 :
Divide $ 3 $ by $ \color{blue}{ 2 } $ and get the remainder

$$ 3 : 2 = 1 \text{ ( remainder is } \color{blue}{ 1 } \text{ ) } $$

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

Step 9 :
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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