Step 1 :
Divide $ 72345 $ by $ 43215 $ and get the remainder

$$ 72345 : 43215 = 1 \text{ ( remainder is } \color{blue}{ 29130 } \text{ ) } $$

The remainder is positive ($ 29130 > 0 $), so we will continue with division.

Step 2 :
Divide $ 43215 $ by $ \color{blue}{ 29130 } $ and get the remainder

$$ 43215 : 29130 = 1 \text{ ( remainder is } \color{blue}{ 14085 } \text{ ) } $$

The remainder is still positive ($ 14085 > 0 $), so we will continue with division.

Step 3 :
Divide $ 29130 $ by $ \color{blue}{ 14085 } $ and get the remainder

$$ 29130 : 14085 = 2 \text{ ( remainder is } \color{blue}{ 960 } \text{ ) } $$

The remainder is still positive ($ 960 > 0 $), so we will continue with division.

Step 4 :
Divide $ 14085 $ by $ \color{blue}{ 960 } $ and get the remainder

$$ 14085 : 960 = 14 \text{ ( remainder is } \color{blue}{ 645 } \text{ ) } $$

The remainder is still positive ($ 645 > 0 $), so we will continue with division.

Step 5 :
Divide $ 960 $ by $ \color{blue}{ 645 } $ and get the remainder

$$ 960 : 645 = 1 \text{ ( remainder is } \color{blue}{ 315 } \text{ ) } $$

The remainder is still positive ($ 315 > 0 $), so we will continue with division.

Step 6 :
Divide $ 645 $ by $ \color{blue}{ 315 } $ and get the remainder

$$ 645 : 315 = 2 \text{ ( remainder is } \color{blue}{ 15 } \text{ ) } $$

The remainder is still positive ($ 15 > 0 $), so we will continue with division.

Step 7 :
Divide $ 315 $ by $ \color{blue}{ 15 } $ and get the remainder

$$ 315 : \color{blue}{ \boxed { 15 }} = 21 \text{ ( remainder is } \color{blue}{ 0 } \text{ ) } $$

The remainder is zero => GCD is the last divisor $ \color{blue}{ \boxed { 15 }} $.

This solution can be visualized using a Venn diagram.

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

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