Step 1 :
Divide $ 7513 $ by $ 6259 $ and get the remainder

$$ 7513 : 6259 = 1 \text{ ( remainder is } \color{blue}{ 1254 } \text{ ) } $$

The remainder is positive ($ 1254 > 0 $), so we will continue with division.

Step 2 :
Divide $ 6259 $ by $ \color{blue}{ 1254 } $ and get the remainder

$$ 6259 : 1254 = 4 \text{ ( remainder is } \color{blue}{ 1243 } \text{ ) } $$

The remainder is still positive ($ 1243 > 0 $), so we will continue with division.

Step 3 :
Divide $ 1254 $ by $ \color{blue}{ 1243 } $ and get the remainder

$$ 1254 : 1243 = 1 \text{ ( remainder is } \color{blue}{ 11 } \text{ ) } $$

The remainder is still positive ($ 11 > 0 $), so we will continue with division.

Step 4 :
Divide $ 1243 $ by $ \color{blue}{ 11 } $ and get the remainder

$$ 1243 : \color{blue}{ \boxed { 11 }} = 113 \text{ ( remainder is } \color{blue}{ 0 } \text{ ) } $$

The remainder is zero => GCD is the last divisor $ \color{blue}{ \boxed { 11 }} $.

This solution can be visualized using a Venn diagram.

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

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