Step 1 : Find prime factorization of each number.

$$\begin{aligned}14300 =& 2\cdot2\cdot5\cdot5\cdot11\cdot13\\[8pt]5915 =& 5\cdot7\cdot13\cdot13\\[8pt]\end{aligned}$$

(view steps on how to factor 14300 and 5915. )

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

$$\begin{aligned}14300 =& 2\cdot2\cdot\color{blue}{\boxed{5}}\cdot5\cdot11\cdot\color{red}{\boxed{13}}\\[8pt]5915 =& \color{blue}{\boxed{5}}\cdot7\cdot\color{red}{\boxed{13}}\cdot13\\[8pt]\end{aligned}$$

Step 3 : Multiply the boxed numbers together:

$$ GCD = 5\cdot13 = 65 $$

This solution can be visualized using a Venn diagram.

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

GCD Calculator