Find Greatest Common Divisor of 1020 and 1170, using prime factorization.

Step 1 : Find prime factorization of each number.

$$\begin{aligned}1020 =& 2\cdot2\cdot3\cdot5\cdot17\\[8pt]1170 =& 2\cdot3\cdot3\cdot5\cdot13\\[8pt]\end{aligned}$$

(view steps on how to factor 1020 and 1170. )

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

$$\begin{aligned}1020 =& \color{blue}{\boxed{2}}\cdot2\cdot\color{red}{\boxed{3}}\cdot\color{Fuchsia}{\boxed{5}}\cdot17\\[8pt]1170 =& \color{blue}{\boxed{2}}\cdot\color{red}{\boxed{3}}\cdot3\cdot\color{Fuchsia}{\boxed{5}}\cdot13\\[8pt]\end{aligned}$$

Step 3 : Multiply the boxed numbers together:

$$ GCD = 2\cdot3\cdot5 = 30 $$

This solution can be visualized using a Venn diagram.

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

GCD Calculator