Step 1 :
Divide $ 85862 $ by $ 16261 $ and get the remainder

$$ 85862 : 16261 = 5 \text{ ( remainder is } \color{blue}{ 4557 } \text{ ) } $$

The remainder is positive ($ 4557 > 0 $), so we will continue with division.

Step 2 :
Divide $ 16261 $ by $ \color{blue}{ 4557 } $ and get the remainder

$$ 16261 : 4557 = 3 \text{ ( remainder is } \color{blue}{ 2590 } \text{ ) } $$

The remainder is still positive ($ 2590 > 0 $), so we will continue with division.

Step 3 :
Divide $ 4557 $ by $ \color{blue}{ 2590 } $ and get the remainder

$$ 4557 : 2590 = 1 \text{ ( remainder is } \color{blue}{ 1967 } \text{ ) } $$

The remainder is still positive ($ 1967 > 0 $), so we will continue with division.

Step 4 :
Divide $ 2590 $ by $ \color{blue}{ 1967 } $ and get the remainder

$$ 2590 : 1967 = 1 \text{ ( remainder is } \color{blue}{ 623 } \text{ ) } $$

The remainder is still positive ($ 623 > 0 $), so we will continue with division.

Step 5 :
Divide $ 1967 $ by $ \color{blue}{ 623 } $ and get the remainder

$$ 1967 : 623 = 3 \text{ ( remainder is } \color{blue}{ 98 } \text{ ) } $$

The remainder is still positive ($ 98 > 0 $), so we will continue with division.

Step 6 :
Divide $ 623 $ by $ \color{blue}{ 98 } $ and get the remainder

$$ 623 : 98 = 6 \text{ ( remainder is } \color{blue}{ 35 } \text{ ) } $$

The remainder is still positive ($ 35 > 0 $), so we will continue with division.

Step 7 :
Divide $ 98 $ by $ \color{blue}{ 35 } $ and get the remainder

$$ 98 : 35 = 2 \text{ ( remainder is } \color{blue}{ 28 } \text{ ) } $$

The remainder is still positive ($ 28 > 0 $), so we will continue with division.

Step 8 :
Divide $ 35 $ by $ \color{blue}{ 28 } $ and get the remainder

$$ 35 : 28 = 1 \text{ ( remainder is } \color{blue}{ 7 } \text{ ) } $$

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

Step 9 :
Divide $ 28 $ by $ \color{blue}{ 7 } $ and get the remainder

$$ 28 : \color{blue}{ \boxed { 7 }} = 4 \text{ ( remainder is } \color{blue}{ 0 } \text{ ) } $$

The remainder is zero => GCD is the last divisor $ \color{blue}{ \boxed { 7 }} $.

This solution can be visualized using a Venn diagram.

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

GCD Calculator