Step 1 : Find prime factorization of each number.

$$\begin{aligned}32756 =& 2\cdot2\cdot19\cdot431\\[8pt]32758 =& 2\cdot11\cdot1489\\[8pt]32760 =& 2\cdot2\cdot2\cdot3\cdot3\cdot5\cdot7\cdot13\\[8pt]\end{aligned}$$

(view steps on how to factor 32756, 32758 and 32760. )

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

$$\begin{aligned}32756 =& \color{blue}{\boxed{2}}\cdot2\cdot19\cdot431\\[8pt]32758 =& \color{blue}{\boxed{2}}\cdot11\cdot1489\\[8pt]32760 =& \color{blue}{\boxed{2}}\cdot2\cdot2\cdot3\cdot3\cdot5\cdot7\cdot13\\[8pt]\end{aligned}$$

Step 3 : Multiply the boxed numbers together:

$$ GCD = 2 $$

This solution can be visualized using a Venn diagram.

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

GCD Calculator