Step 1 :
Divide $ 1552303 $ by $ 233927 $ and get the remainder

$$ 1552303 : 233927 = 6 \text{ ( remainder is } \color{blue}{ 148741 } \text{ ) } $$

The remainder is positive ($ 148741 > 0 $), so we will continue with division.

Step 2 :
Divide $ 233927 $ by $ \color{blue}{ 148741 } $ and get the remainder

$$ 233927 : 148741 = 1 \text{ ( remainder is } \color{blue}{ 85186 } \text{ ) } $$

The remainder is still positive ($ 85186 > 0 $), so we will continue with division.

Step 3 :
Divide $ 148741 $ by $ \color{blue}{ 85186 } $ and get the remainder

$$ 148741 : 85186 = 1 \text{ ( remainder is } \color{blue}{ 63555 } \text{ ) } $$

The remainder is still positive ($ 63555 > 0 $), so we will continue with division.

Step 4 :
Divide $ 85186 $ by $ \color{blue}{ 63555 } $ and get the remainder

$$ 85186 : 63555 = 1 \text{ ( remainder is } \color{blue}{ 21631 } \text{ ) } $$

The remainder is still positive ($ 21631 > 0 $), so we will continue with division.

Step 5 :
Divide $ 63555 $ by $ \color{blue}{ 21631 } $ and get the remainder

$$ 63555 : 21631 = 2 \text{ ( remainder is } \color{blue}{ 20293 } \text{ ) } $$

The remainder is still positive ($ 20293 > 0 $), so we will continue with division.

Step 6 :
Divide $ 21631 $ by $ \color{blue}{ 20293 } $ and get the remainder

$$ 21631 : 20293 = 1 \text{ ( remainder is } \color{blue}{ 1338 } \text{ ) } $$

The remainder is still positive ($ 1338 > 0 $), so we will continue with division.

Step 7 :
Divide $ 20293 $ by $ \color{blue}{ 1338 } $ and get the remainder

$$ 20293 : 1338 = 15 \text{ ( remainder is } \color{blue}{ 223 } \text{ ) } $$

The remainder is still positive ($ 223 > 0 $), so we will continue with division.

Step 8 :
Divide $ 1338 $ by $ \color{blue}{ 223 } $ and get the remainder

$$ 1338 : \color{blue}{ \boxed { 223 }} = 6 \text{ ( remainder is } \color{blue}{ 0 } \text{ ) } $$

The remainder is zero => GCD is the last divisor $ \color{blue}{ \boxed { 223 }} $.

This solution can be visualized using a Venn diagram.

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

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