Step 1 : Find prime factorization of each number.

$$\begin{aligned}21250 =& 2\cdot5\cdot5\cdot5\cdot5\cdot17\\[8pt]16250 =& 2\cdot5\cdot5\cdot5\cdot5\cdot13\\[8pt]\end{aligned}$$

(view steps on how to factor 21250 and 16250. )

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

$$\begin{aligned}21250 =& \color{blue}{\boxed{2}}\cdot\color{red}{\boxed{5}}\cdot\color{Fuchsia}{\boxed{5}}\cdot\color{Orange}{\boxed{5}}\cdot\color{Purple}{\boxed{5}}\cdot17\\[8pt]16250 =& \color{blue}{\boxed{2}}\cdot\color{red}{\boxed{5}}\cdot\color{Fuchsia}{\boxed{5}}\cdot\color{Orange}{\boxed{5}}\cdot\color{Purple}{\boxed{5}}\cdot13\\[8pt]\end{aligned}$$

Step 3 : Multiply the boxed numbers together:

$$ GCD = 2\cdot5\cdot5\cdot5\cdot5 = 1250 $$

This solution can be visualized using a Venn diagram.

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

GCD Calculator