Step 1 :
Divide $ 15472 $ by $ 5264 $ and get the remainder

$$ 15472 : 5264 = 2 \text{ ( remainder is } \color{blue}{ 4944 } \text{ ) } $$

The remainder is positive ($ 4944 > 0 $), so we will continue with division.

Step 2 :
Divide $ 5264 $ by $ \color{blue}{ 4944 } $ and get the remainder

$$ 5264 : 4944 = 1 \text{ ( remainder is } \color{blue}{ 320 } \text{ ) } $$

The remainder is still positive ($ 320 > 0 $), so we will continue with division.

Step 3 :
Divide $ 4944 $ by $ \color{blue}{ 320 } $ and get the remainder

$$ 4944 : 320 = 15 \text{ ( remainder is } \color{blue}{ 144 } \text{ ) } $$

The remainder is still positive ($ 144 > 0 $), so we will continue with division.

Step 4 :
Divide $ 320 $ by $ \color{blue}{ 144 } $ and get the remainder

$$ 320 : 144 = 2 \text{ ( remainder is } \color{blue}{ 32 } \text{ ) } $$

The remainder is still positive ($ 32 > 0 $), so we will continue with division.

Step 5 :
Divide $ 144 $ by $ \color{blue}{ 32 } $ and get the remainder

$$ 144 : 32 = 4 \text{ ( remainder is } \color{blue}{ 16 } \text{ ) } $$

The remainder is still positive ($ 16 > 0 $), so we will continue with division.

Step 6 :
Divide $ 32 $ by $ \color{blue}{ 16 } $ and get the remainder

$$ 32 : \color{blue}{ \boxed { 16 }} = 2 \text{ ( remainder is } \color{blue}{ 0 } \text{ ) } $$

The remainder is zero => GCD is the last divisor $ \color{blue}{ \boxed { 16 }} $.

This solution can be visualized using a Venn diagram.

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

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