Find Greatest Common Divisor of 123456789 and 987654321, using prime factorization.

Step 1 : Find prime factorization of each number.

$$\begin{aligned}123456789 =& 3\cdot3\cdot3607\cdot3803\\[8pt]987654321 =& 3\cdot3\cdot17\cdot17\cdot379721\\[8pt]\end{aligned}$$

(view steps on how to factor 123456789 and 987654321. )

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

$$\begin{aligned}123456789 =& \color{blue}{\boxed{3}}\cdot\color{red}{\boxed{3}}\cdot3607\cdot3803\\[8pt]987654321 =& \color{blue}{\boxed{3}}\cdot\color{red}{\boxed{3}}\cdot17\cdot17\cdot379721\\[8pt]\end{aligned}$$

Step 3 : Multiply the boxed numbers together:

$$ GCD = 3\cdot3 = 9 $$

This solution can be visualized using a Venn diagram.

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

GCD Calculator