Find Greatest Common Divisor of 941688 and 133980, using prime factorization.

Step 1 : Find prime factorization of each number.

$$\begin{aligned}941688 =& 2\cdot2\cdot2\cdot3\cdot3\cdot11\cdot29\cdot41\\[8pt]133980 =& 2\cdot2\cdot3\cdot5\cdot7\cdot11\cdot29\\[8pt]\end{aligned}$$

(view steps on how to factor 941688 and 133980. )

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

$$\begin{aligned}941688 =& \color{blue}{\boxed{2}}\cdot\color{red}{\boxed{2}}\cdot2\cdot\color{Fuchsia}{\boxed{3}}\cdot3\cdot\color{Orange}{\boxed{11}}\cdot\color{Purple}{\boxed{29}}\cdot41\\[8pt]133980 =& \color{blue}{\boxed{2}}\cdot\color{red}{\boxed{2}}\cdot\color{Fuchsia}{\boxed{3}}\cdot5\cdot7\cdot\color{Orange}{\boxed{11}}\cdot\color{Purple}{\boxed{29}}\\[8pt]\end{aligned}$$

Step 3 : Multiply the boxed numbers together:

$$ GCD = 2\cdot2\cdot3\cdot11\cdot29 = 3828 $$

This solution can be visualized using a Venn diagram.

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

GCD Calculator