Step 1 :
Divide $ 3401 $ by $ 542 $ and get the remainder

$$ 3401 : 542 = 6 \text{ ( remainder is } \color{blue}{ 149 } \text{ ) } $$

The remainder is positive ($ 149 > 0 $), so we will continue with division.

Step 2 :
Divide $ 542 $ by $ \color{blue}{ 149 } $ and get the remainder

$$ 542 : 149 = 3 \text{ ( remainder is } \color{blue}{ 95 } \text{ ) } $$

The remainder is still positive ($ 95 > 0 $), so we will continue with division.

Step 3 :
Divide $ 149 $ by $ \color{blue}{ 95 } $ and get the remainder

$$ 149 : 95 = 1 \text{ ( remainder is } \color{blue}{ 54 } \text{ ) } $$

The remainder is still positive ($ 54 > 0 $), so we will continue with division.

Step 4 :
Divide $ 95 $ by $ \color{blue}{ 54 } $ and get the remainder

$$ 95 : 54 = 1 \text{ ( remainder is } \color{blue}{ 41 } \text{ ) } $$

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

Step 5 :
Divide $ 54 $ by $ \color{blue}{ 41 } $ and get the remainder

$$ 54 : 41 = 1 \text{ ( remainder is } \color{blue}{ 13 } \text{ ) } $$

The remainder is still positive ($ 13 > 0 $), so we will continue with division.

Step 6 :
Divide $ 41 $ by $ \color{blue}{ 13 } $ and get the remainder

$$ 41 : 13 = 3 \text{ ( remainder is } \color{blue}{ 2 } \text{ ) } $$

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

Step 7 :
Divide $ 13 $ by $ \color{blue}{ 2 } $ and get the remainder

$$ 13 : 2 = 6 \text{ ( remainder is } \color{blue}{ 1 } \text{ ) } $$

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

Step 8 :
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.

GCD Calculator