Find Greatest Common Divisor of 1430, 650 and 910, using prime factorization.

Step 1 : Find prime factorization of each number.

$$\begin{aligned}1430 =& 2\cdot5\cdot11\cdot13\\[8pt]650 =& 2\cdot5\cdot5\cdot13\\[8pt]910 =& 2\cdot5\cdot7\cdot13\\[8pt]\end{aligned}$$

(view steps on how to factor 1430, 650 and 910. )

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

$$\begin{aligned}1430 =& \color{blue}{\boxed{2}}\cdot\color{red}{\boxed{5}}\cdot11\cdot\color{Fuchsia}{\boxed{13}}\\[8pt]650 =& \color{blue}{\boxed{2}}\cdot\color{red}{\boxed{5}}\cdot5\cdot\color{Fuchsia}{\boxed{13}}\\[8pt]910 =& \color{blue}{\boxed{2}}\cdot\color{red}{\boxed{5}}\cdot7\cdot\color{Fuchsia}{\boxed{13}}\\[8pt]\end{aligned}$$

Step 3 : Multiply the boxed numbers together:

$$ GCD = 2\cdot5\cdot13 = 130 $$

This solution can be visualized using a Venn diagram.

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

GCD Calculator