Step 1 : Find prime factorization of each number.

$$\begin{aligned}9876543210 =& 2\cdot3\cdot3\cdot5\cdot17\cdot17\cdot379721\\[8pt]1234567890 =& 2\cdot3\cdot3\cdot5\cdot3607\cdot3803\\[8pt]\end{aligned}$$

(view steps on how to factor 9876543210 and 1234567890. )

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

$$\begin{aligned}9876543210 =& \color{blue}{\boxed{2}}\cdot\color{red}{\boxed{3}}\cdot\color{Fuchsia}{\boxed{3}}\cdot\color{Orange}{\boxed{5}}\cdot17\cdot17\cdot379721\\[8pt]1234567890 =& \color{blue}{\boxed{2}}\cdot\color{red}{\boxed{3}}\cdot\color{Fuchsia}{\boxed{3}}\cdot\color{Orange}{\boxed{5}}\cdot3607\cdot3803\\[8pt]\end{aligned}$$

Step 3 : Multiply the boxed numbers together:

$$ GCD = 2\cdot3\cdot3\cdot5 = 90 $$

This solution can be visualized using a Venn diagram.

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

GCD Calculator