Find Greatest Common Divisor of 800, 75 and 450, using prime factorization.

Step 1 : Find prime factorization of each number.

$$\begin{aligned}800 =& 2\cdot2\cdot2\cdot2\cdot2\cdot5\cdot5\\[8pt]75 =& 3\cdot5\cdot5\\[8pt]450 =& 2\cdot3\cdot3\cdot5\cdot5\\[8pt]\end{aligned}$$

(view steps on how to factor 800, 75 and 450. )

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

$$\begin{aligned}800 =& 2\cdot2\cdot2\cdot2\cdot2\cdot\color{blue}{\boxed{5}}\cdot\color{red}{\boxed{5}}\\[8pt]75 =& 3\cdot\color{blue}{\boxed{5}}\cdot\color{red}{\boxed{5}}\\[8pt]450 =& 2\cdot3\cdot3\cdot\color{blue}{\boxed{5}}\cdot\color{red}{\boxed{5}}\\[8pt]\end{aligned}$$

Step 3 : Multiply the boxed numbers together:

$$ GCD = 5\cdot5 = 25 $$

This solution can be visualized using a Venn diagram.

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

GCD Calculator