Find Greatest Common Divisor of 40902 and 24140, using prime factorization.

Step 1 : Find prime factorization of each number.

$$\begin{aligned}40902 =& 2\cdot3\cdot17\cdot401\\[8pt]24140 =& 2\cdot2\cdot5\cdot17\cdot71\\[8pt]\end{aligned}$$

(view steps on how to factor 40902 and 24140. )

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

$$\begin{aligned}40902 =& \color{blue}{\boxed{2}}\cdot3\cdot\color{red}{\boxed{17}}\cdot401\\[8pt]24140 =& \color{blue}{\boxed{2}}\cdot2\cdot5\cdot\color{red}{\boxed{17}}\cdot71\\[8pt]\end{aligned}$$

Step 3 : Multiply the boxed numbers together:

$$ GCD = 2\cdot17 = 34 $$

This solution can be visualized using a Venn diagram.

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

GCD Calculator