Find Greatest Common Divisor of 38661640 and 333290000, using prime factorization.

Step 1 : Find prime factorization of each number.

$$\begin{aligned}38661640 =& 2\cdot2\cdot2\cdot5\cdot29\cdot33329\\[8pt]333290000 =& 2\cdot2\cdot2\cdot2\cdot5\cdot5\cdot5\cdot5\cdot33329\\[8pt]\end{aligned}$$

(view steps on how to factor 38661640 and 333290000. )

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

$$\begin{aligned}38661640 =& \color{blue}{\boxed{2}}\cdot\color{red}{\boxed{2}}\cdot\color{Fuchsia}{\boxed{2}}\cdot\color{Orange}{\boxed{5}}\cdot29\cdot\color{Purple}{\boxed{33329}}\\[8pt]333290000 =& \color{blue}{\boxed{2}}\cdot\color{red}{\boxed{2}}\cdot\color{Fuchsia}{\boxed{2}}\cdot2\cdot\color{Orange}{\boxed{5}}\cdot5\cdot5\cdot5\cdot\color{Purple}{\boxed{33329}}\\[8pt]\end{aligned}$$

Step 3 : Multiply the boxed numbers together:

$$ GCD = 2\cdot2\cdot2\cdot5\cdot33329 = 1333160 $$

This solution can be visualized using a Venn diagram.

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

GCD Calculator