Step 1 :
Divide $ 53540 $ by $ 11553 $ and get the remainder

$$ 53540 : 11553 = 4 \text{ ( remainder is } \color{blue}{ 7328 } \text{ ) } $$

The remainder is positive ($ 7328 > 0 $), so we will continue with division.

Step 2 :
Divide $ 11553 $ by $ \color{blue}{ 7328 } $ and get the remainder

$$ 11553 : 7328 = 1 \text{ ( remainder is } \color{blue}{ 4225 } \text{ ) } $$

The remainder is still positive ($ 4225 > 0 $), so we will continue with division.

Step 3 :
Divide $ 7328 $ by $ \color{blue}{ 4225 } $ and get the remainder

$$ 7328 : 4225 = 1 \text{ ( remainder is } \color{blue}{ 3103 } \text{ ) } $$

The remainder is still positive ($ 3103 > 0 $), so we will continue with division.

Step 4 :
Divide $ 4225 $ by $ \color{blue}{ 3103 } $ and get the remainder

$$ 4225 : 3103 = 1 \text{ ( remainder is } \color{blue}{ 1122 } \text{ ) } $$

The remainder is still positive ($ 1122 > 0 $), so we will continue with division.

Step 5 :
Divide $ 3103 $ by $ \color{blue}{ 1122 } $ and get the remainder

$$ 3103 : 1122 = 2 \text{ ( remainder is } \color{blue}{ 859 } \text{ ) } $$

The remainder is still positive ($ 859 > 0 $), so we will continue with division.

Step 6 :
Divide $ 1122 $ by $ \color{blue}{ 859 } $ and get the remainder

$$ 1122 : 859 = 1 \text{ ( remainder is } \color{blue}{ 263 } \text{ ) } $$

The remainder is still positive ($ 263 > 0 $), so we will continue with division.

Step 7 :
Divide $ 859 $ by $ \color{blue}{ 263 } $ and get the remainder

$$ 859 : 263 = 3 \text{ ( remainder is } \color{blue}{ 70 } \text{ ) } $$

The remainder is still positive ($ 70 > 0 $), so we will continue with division.

Step 8 :
Divide $ 263 $ by $ \color{blue}{ 70 } $ and get the remainder

$$ 263 : 70 = 3 \text{ ( remainder is } \color{blue}{ 53 } \text{ ) } $$

The remainder is still positive ($ 53 > 0 $), so we will continue with division.

Step 9 :
Divide $ 70 $ by $ \color{blue}{ 53 } $ and get the remainder

$$ 70 : 53 = 1 \text{ ( remainder is } \color{blue}{ 17 } \text{ ) } $$

The remainder is still positive ($ 17 > 0 $), so we will continue with division.

Step 10 :
Divide $ 53 $ by $ \color{blue}{ 17 } $ and get the remainder

$$ 53 : 17 = 3 \text{ ( remainder is } \color{blue}{ 2 } \text{ ) } $$

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

Step 11 :
Divide $ 17 $ by $ \color{blue}{ 2 } $ and get the remainder

$$ 17 : 2 = 8 \text{ ( remainder is } \color{blue}{ 1 } \text{ ) } $$

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

Step 12 :
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