Find Greatest Common Divisor of 35742 and 13566, using prime factorization.

Step 1 : Find prime factorization of each number.

$$\begin{aligned}35742 =& 2\cdot3\cdot7\cdot23\cdot37\\[8pt]13566 =& 2\cdot3\cdot7\cdot17\cdot19\\[8pt]\end{aligned}$$

(view steps on how to factor 35742 and 13566. )

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

$$\begin{aligned}35742 =& \color{blue}{\boxed{2}}\cdot\color{red}{\boxed{3}}\cdot\color{Fuchsia}{\boxed{7}}\cdot23\cdot37\\[8pt]13566 =& \color{blue}{\boxed{2}}\cdot\color{red}{\boxed{3}}\cdot\color{Fuchsia}{\boxed{7}}\cdot17\cdot19\\[8pt]\end{aligned}$$

Step 3 : Multiply the boxed numbers together:

$$ GCD = 2\cdot3\cdot7 = 42 $$

This solution can be visualized using a Venn diagram.

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

GCD Calculator