Step 1 : Find prime factorization of each number.

$$\begin{aligned}87171 =& 3\cdot7\cdot7\cdot593\\[8pt]1624350 =& 2\cdot3\cdot5\cdot5\cdot7\cdot7\cdot13\cdot17\\[8pt]\end{aligned}$$

(view steps on how to factor 87171 and 1624350. )

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

$$\begin{aligned}87171 =& \color{blue}{\boxed{3}}\cdot\color{red}{\boxed{7}}\cdot\color{Fuchsia}{\boxed{7}}\cdot593\\[8pt]1624350 =& 2\cdot\color{blue}{\boxed{3}}\cdot5\cdot5\cdot\color{red}{\boxed{7}}\cdot\color{Fuchsia}{\boxed{7}}\cdot13\cdot17\\[8pt]\end{aligned}$$

Step 3 : Multiply the boxed numbers together:

$$ GCD = 3\cdot7\cdot7 = 147 $$

This solution can be visualized using a Venn diagram.

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

GCD Calculator