Find Greatest Common Divisor of 45, 50 and 60, using prime factorization.

Step 1 : Find prime factorization of each number.

$$\begin{aligned}45 =& 3\cdot3\cdot5\\[8pt]50 =& 2\cdot5\cdot5\\[8pt]60 =& 2\cdot2\cdot3\cdot5\\[8pt]\end{aligned}$$

(view steps on how to factor 45, 50 and 60. )

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

$$\begin{aligned}45 =& 3\cdot3\cdot\color{blue}{\boxed{5}}\\[8pt]50 =& 2\cdot\color{blue}{\boxed{5}}\cdot5\\[8pt]60 =& 2\cdot2\cdot3\cdot\color{blue}{\boxed{5}}\\[8pt]\end{aligned}$$

Step 3 : Multiply the boxed numbers together:

$$ GCD = 5 $$

This solution can be visualized using a Venn diagram.

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

GCD Calculator