Find Greatest Common Divisor of 1204 and 2400, using prime factorization.

Step 1 : Find prime factorization of each number.

$$\begin{aligned}1204 =& 2\cdot2\cdot7\cdot43\\[8pt]2400 =& 2\cdot2\cdot2\cdot2\cdot2\cdot3\cdot5\cdot5\\[8pt]\end{aligned}$$

(view steps on how to factor 1204 and 2400. )

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

$$\begin{aligned}1204 =& \color{blue}{\boxed{2}}\cdot\color{red}{\boxed{2}}\cdot7\cdot43\\[8pt]2400 =& \color{blue}{\boxed{2}}\cdot\color{red}{\boxed{2}}\cdot2\cdot2\cdot2\cdot3\cdot5\cdot5\\[8pt]\end{aligned}$$

Step 3 : Multiply the boxed numbers together:

$$ GCD = 2\cdot2 = 4 $$

This solution can be visualized using a Venn diagram.

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

GCD Calculator