Step 1 :
Divide $ 1692 $ by $ 1401 $ and get the remainder

$$ 1692 : 1401 = 1 \text{ ( remainder is } \color{blue}{ 291 } \text{ ) } $$

The remainder is positive ($ 291 > 0 $), so we will continue with division.

Step 2 :
Divide $ 1401 $ by $ \color{blue}{ 291 } $ and get the remainder

$$ 1401 : 291 = 4 \text{ ( remainder is } \color{blue}{ 237 } \text{ ) } $$

The remainder is still positive ($ 237 > 0 $), so we will continue with division.

Step 3 :
Divide $ 291 $ by $ \color{blue}{ 237 } $ and get the remainder

$$ 291 : 237 = 1 \text{ ( remainder is } \color{blue}{ 54 } \text{ ) } $$

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

Step 4 :
Divide $ 237 $ by $ \color{blue}{ 54 } $ and get the remainder

$$ 237 : 54 = 4 \text{ ( remainder is } \color{blue}{ 21 } \text{ ) } $$

The remainder is still positive ($ 21 > 0 $), so we will continue with division.

Step 5 :
Divide $ 54 $ by $ \color{blue}{ 21 } $ and get the remainder

$$ 54 : 21 = 2 \text{ ( remainder is } \color{blue}{ 12 } \text{ ) } $$

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

Step 6 :
Divide $ 21 $ by $ \color{blue}{ 12 } $ and get the remainder

$$ 21 : 12 = 1 \text{ ( remainder is } \color{blue}{ 9 } \text{ ) } $$

The remainder is still positive ($ 9 > 0 $), so we will continue with division.

Step 7 :
Divide $ 12 $ by $ \color{blue}{ 9 } $ and get the remainder

$$ 12 : 9 = 1 \text{ ( remainder is } \color{blue}{ 3 } \text{ ) } $$

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

Step 8 :
Divide $ 9 $ by $ \color{blue}{ 3 } $ and get the remainder

$$ 9 : \color{blue}{ \boxed { 3 }} = 3 \text{ ( remainder is } \color{blue}{ 0 } \text{ ) } $$

The remainder is zero => GCD is the last divisor $ \color{blue}{ \boxed { 3 }} $.

This solution can be visualized using a Venn diagram.

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

GCD Calculator