Step 1 :
Divide $ 2576 $ by $ 943 $ and get the remainder

$$ 2576 : 943 = 2 \text{ ( remainder is } \color{blue}{ 690 } \text{ ) } $$

The remainder is positive ($ 690 > 0 $), so we will continue with division.

Step 2 :
Divide $ 943 $ by $ \color{blue}{ 690 } $ and get the remainder

$$ 943 : 690 = 1 \text{ ( remainder is } \color{blue}{ 253 } \text{ ) } $$

The remainder is still positive ($ 253 > 0 $), so we will continue with division.

Step 3 :
Divide $ 690 $ by $ \color{blue}{ 253 } $ and get the remainder

$$ 690 : 253 = 2 \text{ ( remainder is } \color{blue}{ 184 } \text{ ) } $$

The remainder is still positive ($ 184 > 0 $), so we will continue with division.

Step 4 :
Divide $ 253 $ by $ \color{blue}{ 184 } $ and get the remainder

$$ 253 : 184 = 1 \text{ ( remainder is } \color{blue}{ 69 } \text{ ) } $$

The remainder is still positive ($ 69 > 0 $), so we will continue with division.

Step 5 :
Divide $ 184 $ by $ \color{blue}{ 69 } $ and get the remainder

$$ 184 : 69 = 2 \text{ ( remainder is } \color{blue}{ 46 } \text{ ) } $$

The remainder is still positive ($ 46 > 0 $), so we will continue with division.

Step 6 :
Divide $ 69 $ by $ \color{blue}{ 46 } $ and get the remainder

$$ 69 : 46 = 1 \text{ ( remainder is } \color{blue}{ 23 } \text{ ) } $$

The remainder is still positive ($ 23 > 0 $), so we will continue with division.

Step 7 :
Divide $ 46 $ by $ \color{blue}{ 23 } $ and get the remainder

$$ 46 : \color{blue}{ \boxed { 23 }} = 2 \text{ ( remainder is } \color{blue}{ 0 } \text{ ) } $$

The remainder is zero => GCD is the last divisor $ \color{blue}{ \boxed { 23 }} $.

This solution can be visualized using a Venn diagram.

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

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