Step 1 : Find prime factorization of each number.

$$\begin{aligned}59840 =& 2\cdot2\cdot2\cdot2\cdot2\cdot2\cdot5\cdot11\cdot17\\[8pt]85327 =& 11\cdot7757\\[8pt]\end{aligned}$$

(view steps on how to factor 59840 and 85327. )

Step 2 : Put a box around factors that are common for all numbers:

$$\begin{aligned}59840 =& 2\cdot2\cdot2\cdot2\cdot2\cdot2\cdot5\cdot\color{blue}{\boxed{11}}\cdot17\\[8pt]85327 =& \color{blue}{\boxed{11}}\cdot7757\\[8pt]\end{aligned}$$

Step 3 : Multiply the boxed numbers together:

$$ GCD = 11 $$

This solution can be visualized using a Venn diagram.

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

GCD Calculator