Step 1 :
Divide $ 80045 $ by $ 5302 $ and get the remainder

$$ 80045 : 5302 = 15 \text{ ( remainder is } \color{blue}{ 515 } \text{ ) } $$

The remainder is positive ($ 515 > 0 $), so we will continue with division.

Step 2 :
Divide $ 5302 $ by $ \color{blue}{ 515 } $ and get the remainder

$$ 5302 : 515 = 10 \text{ ( remainder is } \color{blue}{ 152 } \text{ ) } $$

The remainder is still positive ($ 152 > 0 $), so we will continue with division.

Step 3 :
Divide $ 515 $ by $ \color{blue}{ 152 } $ and get the remainder

$$ 515 : 152 = 3 \text{ ( remainder is } \color{blue}{ 59 } \text{ ) } $$

The remainder is still positive ($ 59 > 0 $), so we will continue with division.

Step 4 :
Divide $ 152 $ by $ \color{blue}{ 59 } $ and get the remainder

$$ 152 : 59 = 2 \text{ ( remainder is } \color{blue}{ 34 } \text{ ) } $$

The remainder is still positive ($ 34 > 0 $), so we will continue with division.

Step 5 :
Divide $ 59 $ by $ \color{blue}{ 34 } $ and get the remainder

$$ 59 : 34 = 1 \text{ ( remainder is } \color{blue}{ 25 } \text{ ) } $$

The remainder is still positive ($ 25 > 0 $), so we will continue with division.

Step 6 :
Divide $ 34 $ by $ \color{blue}{ 25 } $ and get the remainder

$$ 34 : 25 = 1 \text{ ( remainder is } \color{blue}{ 9 } \text{ ) } $$

The remainder is still positive ($ 9 > 0 $), so we will continue with division.

Step 7 :
Divide $ 25 $ by $ \color{blue}{ 9 } $ and get the remainder

$$ 25 : 9 = 2 \text{ ( remainder is } \color{blue}{ 7 } \text{ ) } $$

The remainder is still positive ($ 7 > 0 $), so we will continue with division.

Step 8 :
Divide $ 9 $ by $ \color{blue}{ 7 } $ and get the remainder

$$ 9 : 7 = 1 \text{ ( remainder is } \color{blue}{ 2 } \text{ ) } $$

The remainder is still positive ($ 2 > 0 $), so we will continue with division.

Step 9 :
Divide $ 7 $ by $ \color{blue}{ 2 } $ and get the remainder

$$ 7 : 2 = 3 \text{ ( remainder is } \color{blue}{ 1 } \text{ ) } $$

The remainder is still positive ($ 1 > 0 $), so we will continue with division.

Step 10 :
Divide $ 2 $ by $ \color{blue}{ 1 } $ and get the remainder

$$ 2 : \color{blue}{ \boxed { 1 }} = 2 \text{ ( remainder is } \color{blue}{ 0 } \text{ ) } $$

The remainder is zero => GCD is the last divisor $ \color{blue}{ \boxed { 1 }} $.

This solution can be visualized using a Venn diagram.

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

GCD Calculator