Find Greatest Common Divisor of 24140 and 16762, using prime factorization.

Step 1 : Find prime factorization of each number.

$$\begin{aligned}24140 =& 2\cdot2\cdot5\cdot17\cdot71\\[8pt]16762 =& 2\cdot17\cdot17\cdot29\\[8pt]\end{aligned}$$

(view steps on how to factor 24140 and 16762. )

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

$$\begin{aligned}24140 =& \color{blue}{\boxed{2}}\cdot2\cdot5\cdot\color{red}{\boxed{17}}\cdot71\\[8pt]16762 =& \color{blue}{\boxed{2}}\cdot\color{red}{\boxed{17}}\cdot17\cdot29\\[8pt]\end{aligned}$$

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